Relations and Functions



Popular Tutorials in Relations and Functions

    • What's a Function?What's a Function?

    What's a Function?

    Function rules are like instructions on how to change input values into their respective output values. In this tutorial, see how to write a function rule for a given relation. Check it out!

    • How Can You Tell if a Relation is Not a Function?How Can You Tell if a Relation is Not a Function?

    How Can You Tell if a Relation is Not a Function?

    Every function is a relation, but not every relation is a function! Watch this video to learn how to tell which relations are functions and which are not.

    • How Do You Graph a Linear Equation From a Table?How Do You Graph a Linear Equation From a Table?

    How Do You Graph a Linear Equation From a Table?

    A table of values for a linear equation can be very helpful, but a graph of the equation can be even better! In this tutorial, you'll see how to use a table of values to graph a linear equation!

    • How is a Function Defined?How is a Function Defined?

    How is a Function Defined?

    You can't go through algebra without learning about functions. This tutorial shows you the definition of a function and gives you an example of a function. Take a look!

    • What is a Linear Function?What is a Linear Function?
    • How Do You Find the Y-Coordinate of a Point on a Line If You Have a Graph?How Do You Find the Y-Coordinate of a Point on a Line If You Have a Graph?

    How Do You Find the Y-Coordinate of a Point on a Line If You Have a Graph?

    Looking at the graph of an equation? Trying to figure out the y-value of a point on that graph? Learn how to answer that question by watching this tutorial! This tutorial shows you how to use the graph of a equation to find the y-value of a point.

    • How Do You Check if a Point is on a Line If You Have an Equation?How Do You Check if a Point is on a Line If You Have an Equation?

    How Do You Check if a Point is on a Line If You Have an Equation?

    Wondering if a point is part of the equation of a line? Got the equation of the line but no graph? No problem! Just take that point and plug it into the equation and simplify. If you end up with a true statement, the point is indeed part of the equation. If you end up with a false statement, then that point is not part of the equation. See this process first-hand in this tutorial!

    • How Do You Check if a Point is on a Line If You Have a Graph?How Do You Check if a Point is on a Line If You Have a Graph?

    How Do You Check if a Point is on a Line If You Have a Graph?

    Wonder if a point is part of a line? You could take that equation and graph it. Then use the graph to get your answer! Watch how in this tutorial.

    • How Do You Find the Common Difference in an Arithmetic Sequence?How Do You Find the Common Difference in an Arithmetic Sequence?

    How Do You Find the Common Difference in an Arithmetic Sequence?

    Trying to find the common difference in an arithmetic sequence? You need to figure out what number you need to add to each term to get the next term in the sequence. It's easier than you might think! Watch this tutorial and learn how to find the common difference in an arithmetic sequence.

    • How Do You Find the Next Terms in an Arithmetic Sequence?How Do You Find the Next Terms in an Arithmetic Sequence?

    How Do You Find the Next Terms in an Arithmetic Sequence?

    To find the next few terms in an arithmetic sequence, you first need to find the common difference, the constant amount of change between numbers in an arithmetic sequence. Once you know the common difference, you can use it to find those next terms! This tutorial takes you through that process, so be sure to check it out!

    • How Do You Find the Nth Term in an Arithmetic Sequence?How Do You Find the Nth Term in an Arithmetic Sequence?

    How Do You Find the Nth Term in an Arithmetic Sequence?

    Got an arithmetic sequence? Trying to find a later term in that sequence? Don't want to keep adding the common difference to each term until you get to the one you want? Then use the equation for the nth term in an arithmetic sequence instead! This tutorial will show you how!

    • What's the Zero of a Function?What's the Zero of a Function?

    What's the Zero of a Function?

    The zero of a function is the x-value that makes the function equal to 0. In this tutorial, you'll learn about the zero of a function and see how to find it in an example. Take a look!

    • What's an Arithmetic Sequence?What's an Arithmetic Sequence?

    What's an Arithmetic Sequence?

    See a pattern in a sequence? It might be an arithmetic sequence! Learn about arithmetic sequences by watching this tutorial.

    • What's the Common Difference?What's the Common Difference?

    What's the Common Difference?

    Did you know that the constant you add to a term in an arithmetic sequence to get the next term has a name? It's called a common difference! This tutorial is a great way to learn more about the common difference of an arithmetic sequence.

    • What's a Sequence?What's a Sequence?

    What's a Sequence?

    Got a set of numbers? Are they in a particular order? If so, then you have a sequence! Take a look at sequences by watching this tutorial.

    • What's a Term in a Sequence?What's a Term in a Sequence?

    What's a Term in a Sequence?

    When you're looking at a sequence, each value in that sequence is called a term. This tutorial explains the definition of the term of a sequence. Take a look!

    • What Are Dependent and Independent Variables?What Are Dependent and Independent Variables?
    • Where Does the Formula for a Term in an Arithmetic Sequence Come From?Where Does the Formula for a Term in an Arithmetic Sequence Come From?

    Where Does the Formula for a Term in an Arithmetic Sequence Come From?

    Trying to find the value of a certain term in an arithmetic sequence? Don't want to go through the terms one-by-one to find the one you want? Use the formula to find the nth term in an arithmetic sequence! This tutorial shows you how find that formula!

    • How Do You Make an Approximate Graph From a Word Problem?How Do You Make an Approximate Graph From a Word Problem?

    How Do You Make an Approximate Graph From a Word Problem?

    Sometimes a word problem describes a situation that can be better understood if it were graphed. This tutorial gives an example of one such word problem. Check it out!

    • How Do You Plot Points in the Coordinate Plane?How Do You Plot Points in the Coordinate Plane?

    How Do You Plot Points in the Coordinate Plane?

    Knowing how to plot ordered pairs is an essential part of graphing functions. In this tutorial, you'll see how to take an ordered pair and plot it on the coordinate plane. Take a look!

    • How Do You Write a Relation from a Word Problem?How Do You Write a Relation from a Word Problem?

    How Do You Write a Relation from a Word Problem?

    Word problems are a great way to see math in action! In this tutorial, see how to write a relation from the information given in a word problem. Then, plot the points in the relation to get a graph that shows the relation!

    • How Do You Use the Graph of a Linear Equation to Solve a Word Problem?How Do You Use the Graph of a Linear Equation to Solve a Word Problem?

    How Do You Use the Graph of a Linear Equation to Solve a Word Problem?

    Word problems are a great way to see math in the real world! In this tutorial, see how to figure out how long it will take for a rabbit population to go extinct. You'll also see how to set up a table and a graph to help find the answer!

    • How Do You Solve a Word Problem Using a Function?How Do You Solve a Word Problem Using a Function?

    How Do You Solve a Word Problem Using a Function?

    Word problems are a great way to see math in action! This word problem deals with calculating profit after a certain number of years. See how to use a function from the word problem to solve!

    • How Do You Find the Domain and Range of a Relation?How Do You Find the Domain and Range of a Relation?

    How Do You Find the Domain and Range of a Relation?

    Finding the domain and range of a relation? No problem! Watch this tutorial and learn how to find the domain and range of a relation.

    • How Do You Find the Domain and Range of the Inverse of a Relation?How Do You Find the Domain and Range of the Inverse of a Relation?

    How Do You Find the Domain and Range of the Inverse of a Relation?

    Finding the domain and range of the inverse of a relation can be tricky, unless you know the correct steps! This tutorial shows you the steps needed to find the domain and range of the inverse of a relation. Check it out!

    • How Do You Find the Solution Set for a Relation If You Know the Domain?How Do You Find the Solution Set for a Relation If You Know the Domain?

    How Do You Find the Solution Set for a Relation If You Know the Domain?

    To find the solution set of an equation with a given domain, you first need to plug each value in the domain into the equation to get the respective range values. Create ordered pairs from these values and write them as a set. That set is your answer! Learn it all in this tutorial!

    • How Do You Graph a Linear Equation in Slope-Intercept Form by Making a Table?How Do You Graph a Linear Equation in Slope-Intercept Form by Making a Table?

    How Do You Graph a Linear Equation in Slope-Intercept Form by Making a Table?

    Graphing a function? It would be really helpful if you had a table of values that fit your equation. You could plot those values on a coordinate plane and connect the point to make your graph. See it all in this tutorial!

    • How Can You Tell If You Have a Linear Equation?How Can You Tell If You Have a Linear Equation?

    How Can You Tell If You Have a Linear Equation?

    Trying to figure out if an equation is a linear equation? Well, can you write it in standard form? If you can, then it's a linear equation. See this process in action by watching this tutorial!

    • How Do You Figure Out If a Relation is a Function?How Do You Figure Out If a Relation is a Function?

    How Do You Figure Out If a Relation is a Function?

    How do you figure out if a relation is a function? You could set up the relation as a table of ordered pairs. Then, test to see if each element in the domain is matched with exactly one element in the range. If so, you have a function! Watch this tutorial to see how you can determine if a relation is a function.

    • How Do You Use the Vertical Line Test to Figure Out if a Graph is a Function?How Do You Use the Vertical Line Test to Figure Out if a Graph is a Function?

    How Do You Use the Vertical Line Test to Figure Out if a Graph is a Function?

    Trying to figure out if an equation is a function? Graph it and perform the vertical line test. If it passes, then it's a function! Get some practice by watching this tutorial!

    • How Do You Find f(x) If You Have a Value For x?How Do You Find f(x) If You Have a Value For x?

    How Do You Find f(x) If You Have a Value For x?

    To solve a function for a given value, plug that value into the function and simplify. See this first-hand by watching this tutorial!

    • What is an Ordered Pair?What is an Ordered Pair?

    What is an Ordered Pair?

    Ordered pairs are a fundamental part of graphing. Ordered pairs make up functions on a graph, and very often, you need to plot ordered pairs in order to see what the graph of a function looks like. This tutorial will introduce you to ordered pairs!

    • What is the Origin?What is the Origin?

    What is the Origin?

    The coordinate plane has two axes: the horizontal and vertical axes. These two axes intersect one another at a point called the origin. Learn about the ordered pair that indicates the origin and its location in the coordinate plane by watching this tutorial!

    • What is a Relation?What is a Relation?

    What is a Relation?

    Got a set of ordered pairs? Then you have a relation! This tutorial takes a look at relations!

    • What is Domain?What is Domain?

    What is Domain?

    Did you know that a relation has a domain? The domain of a relation is the set of the first coordinates from the ordered pairs. This tutorial defines the domain of a relation!

    • What is Range?What is Range?

    What is Range?

    Did you know that a relation has a range? The range of a relation is the set of the second coordinates from the ordered pairs. This tutorial defines the range of a relation!

    • What's the Inverse of a Relation?What's the Inverse of a Relation?

    What's the Inverse of a Relation?

    Did you know there's something called the inverse of a relation? Watch this tutorial to learn the definition for the inverse of a relation and to see an example!

    • What's a Solution Set?What's a Solution Set?

    What's a Solution Set?

    When an equation has two variables, the set of ordered pairs that are the solution to the equation are called the solution set to the equation. In this tutorial, you'll learn the definition of a solution set and see an example. Take a look!

    • What's Standard Form of a Linear Equation?What's Standard Form of a Linear Equation?

    What's Standard Form of a Linear Equation?

    A linear equation can be written in many different forms, and each of them is quite useful! One of these is standard form. Watch this tutorial and learn the standard form for a linear equation!

    • What's a Function?What's a Function?

    What's a Function?

    You can't go through algebra without learning about functions. This tutorial shows you a great approach to thinking about functions! Learn the definition of a function and see the different ways functions can be represented. Take a look!

    • What's the Vertical Line Test?What's the Vertical Line Test?

    What's the Vertical Line Test?

    Even graphs need to worry about tests! Using the vertical line test, you can figure out if a graph is a function or not. Watch this tutorial and learn about the vertical line test. Then, put your graphs to the test!

    • What is Function Notation?What is Function Notation?

    What is Function Notation?

    Every see 'f(x)' in your math? That's function notation! It's a way to indicate that an equation is a function. Learn about function notation by watching this tutorial.

    • What is the Coordinate Plane?What is the Coordinate Plane?

    What is the Coordinate Plane?

    You can't graph a function or plot ordered pairs without a coordinate plane! Learn about the coordinate plane by watching this tutorial.

    • What are Quadrants in the Coordinate Plane?What are Quadrants in the Coordinate Plane?

    What are Quadrants in the Coordinate Plane?

    Did you know that there are four quadrants that help make up the coordinate plane? Learn about these quadrants, and what ordered pairs are located in each, by watching this tutorial!

    • Why Is It Called an Ordered Pair?Why Is It Called an Ordered Pair?

    Why Is It Called an Ordered Pair?

    Why is an ordered pair called an ordered pair? Because order is important! If an ordered pair is written in a different order, it makes a different ordered pair. This tutorial shows you why order is important when you're dealing with ordered pairs.

    • What is the X-Coordinate?What is the X-Coordinate?

    What is the X-Coordinate?

    Ordered pairs are a crucial part of graphing, but you need to know how to identify the coordinates in an ordered pair if you're going to plot it on a coordinate plane. In this tutorial, you'll see how to identify the x-coordinate in an ordered pair!

    • What is the Y-Coordinate?What is the Y-Coordinate?

    What is the Y-Coordinate?

    Ordered pairs are a crucial part of graphing, but you need to know how to identify the coordinates in an ordered pair if you're going to plot it on a coordinate plane. In this tutorial, you'll see how to identify the y-coordinate in an ordered pair!

    • What is the X-Axis?What is the X-Axis?

    What is the X-Axis?

    To graph a function or plot an ordered pair, you need to use a coordinate plane, so you should learn all about it! In this tutorial, you'll learn about the x-axis and see where it's located in the coordinate plane.

    • What is the Y-Axis?What is the Y-Axis?

    What is the Y-Axis?

    To graph a function or plot an ordered pair, you need to use a coordinate plane, so you should learn all about it! In this tutorial, you'll learn about the y-axis and see where it's located in the coordinate plane.

    • What are the Coordinate Axes?What are the Coordinate Axes?

    What are the Coordinate Axes?

    The coordinate plane has two axes: the horizontal and vertical axes. Learn about these axes and the name for their point of intersection by watching this tutorial!

    • What is a Continuous Function?What is a Continuous Function?

    What is a Continuous Function?

    You've probably seen a continuous function before and not even known it! In this tutorial, you'll learn what a continuous function is and what a graph needs to have in order to be continuous.

    • What is a Constant Function?What is a Constant Function?

    What is a Constant Function?

    Have you ever seen a horizontal line? Then you've seen a constant function! This tutorial introduces constant functions and shows you examples of their equations and graphs!

    • What is a Parent Function?What is a Parent Function?

    What is a Parent Function?

    Did you know that functions have parents too? Follow along with this tutorial to learn about families of functions and their parent function!

    • How Do You Identify Points on a Graph?How Do You Identify Points on a Graph?

    How Do You Identify Points on a Graph?

    Plotting points on the coordinate plane is the foundation of graphing equations! But before you can graph equations, you should be very familiar with the coordinate plane. In this tutorial, you'll see how to identify the ordered pair of a point on the coordinate plane. Plus, see how to figure out which quadrant the point is in!

    • How Do You Make a Figure Larger Using a Dilation?How Do You Make a Figure Larger Using a Dilation?

    How Do You Make a Figure Larger Using a Dilation?

    Dilation allows you to shrink or enlarge the size of a figure without changing its shape. In this tutorial, follow along as you see how dilate a figure by a given scale factor. Check it out!

    • What is a Dilation?What is a Dilation?

    What is a Dilation?

    When someone's eyes dilate, their pupils get bigger or smaller, but they always stay the same shape. Dilation in math is very similar. When you dilate a figure, you change the size of the figure without changing its shape. This tutorial introduces you to dilation. Take a look!

    • How Do You Make a Table of Values for a Linear Equation?How Do You Make a Table of Values for a Linear Equation?

    How Do You Make a Table of Values for a Linear Equation?

    To graph a linear equation, you could make a table of values to plot, but first you'll need to know how to make the table. Take a look at this tutorial! You'll see how to set up a table, choose appropriate x-values, plug those values into the equation, and simplify to get the respective y-values. This tutorial shows you how to set up a table of values for a linear equation!

    • What is a Linear Equation?What is a Linear Equation?

    What is a Linear Equation?

    If you're learning about graphs, you're bound to see a bunch of linear equations, so it's a good idea to understand what makes an equation a linear equation. This tutorial explains linear equations and shows you the difference between equations that are linear and ones that are not. Check it out!

    • How Do You Use a Graph to Reflect a Figure Over the Y-Axis?How Do You Use a Graph to Reflect a Figure Over the Y-Axis?

    How Do You Use a Graph to Reflect a Figure Over the Y-Axis?

    Reflecting a figure over the y-axis can be a little tricky, unless you have a plan. In this tutorial, see how to use the graph of a figure to perform the reflection. Check it out!

    • How Do You Use Coordinates to Reflect a Figure Over the X-Axis?How Do You Use Coordinates to Reflect a Figure Over the X-Axis?

    How Do You Use Coordinates to Reflect a Figure Over the X-Axis?

    Want to see how to reflect a figure over the x-axis? Then this tutorial was made for you! In this tutorial, you'll see how to use coordinates from the original figure to reflect the figure over the x-axis. Take a look!

    • How Do You Use Coordinates to Reflect a Figure Over the Y-Axis?How Do You Use Coordinates to Reflect a Figure Over the Y-Axis?

    How Do You Use Coordinates to Reflect a Figure Over the Y-Axis?

    Want to see how to reflect a figure over the y-axis? Then this tutorial was made for you! In this tutorial, you'll see how to use coordinates from the original figure to reflect the figure over the y-axis. Take a look!

    • How Do You Use a Graph to Reflect a Figure Over the X-Axis?How Do You Use a Graph to Reflect a Figure Over the X-Axis?

    How Do You Use a Graph to Reflect a Figure Over the X-Axis?

    Reflecting a figure over the x-axis can be a little tricky, unless you have a plan. In this tutorial, see how to use the graph of a figure to perform the reflection. Check it out!

    • How Do You Rotate a Figure 90 Degrees Around the Origin?How Do You Rotate a Figure 90 Degrees Around the Origin?

    How Do You Rotate a Figure 90 Degrees Around the Origin?

    Rotating a figure about the origin can be a little tricky, but this tutorial can help! This tutorial shows you how to rotate coordinates from the original figure about the origin. Then, simply connect the points to create the new figure. See this process in action by watching this tutorial!

    • How Do You Rotate a Figure 180 Degrees Around the Origin?How Do You Rotate a Figure 180 Degrees Around the Origin?

    How Do You Rotate a Figure 180 Degrees Around the Origin?

    Rotating a figure about the origin can be a little tricky, but this tutorial can help! This tutorial shows you how to rotate coordinates from the original figure about the origin. Then, simply connect the points to create the new figure. See this process in action by watching this tutorial!

    • How Do You Rotate a Figure 270 Degrees Around the Origin?How Do You Rotate a Figure 270 Degrees Around the Origin?

    How Do You Rotate a Figure 270 Degrees Around the Origin?

    Rotating a figure about the origin can be a little tricky, but this tutorial can help! This tutorial shows you how to rotate coordinates from the original figure about the origin. Then, simply connect the points to create the new figure. See this process in action by watching this tutorial!

    • How Do You Use a Graph to Translate a Figure Horizontally?How Do You Use a Graph to Translate a Figure Horizontally?

    How Do You Use a Graph to Translate a Figure Horizontally?

    Translating a figure on the coordinate plane is easier than you might think! In this tutorial, see how to use the graph of the original figure to perform the translation. Take a look!

    • How Do You Use a Graph to Translate a Figure Vertically?How Do You Use a Graph to Translate a Figure Vertically?

    How Do You Use a Graph to Translate a Figure Vertically?

    Translating a figure on the coordinate plane is easier than you might think! In this tutorial, see how to use the graph of the original figure to perform the translation. Take a look!

    • How Do You Use a Graph to Translate a Figure Diagonally?How Do You Use a Graph to Translate a Figure Diagonally?

    How Do You Use a Graph to Translate a Figure Diagonally?

    Performing multiple translations on the graph of a figure is easier than you might think! In this tutorial, see how to use the graph of the original figure to perform each translation in order to get the graph of the new figure. Check it out!

    • How Do You Use Coordinates to Translate a Figure Horizontally?How Do You Use Coordinates to Translate a Figure Horizontally?

    How Do You Use Coordinates to Translate a Figure Horizontally?

    Translating a figure on the coordinate plane is easier than you might think! This tutorial shows you how to translate coordinates from the original figure. Then, simply connect the points to create your new figure. This tutorial shows you how!

    • How Do You Use Coordinates to Translate a Figure Vertically?How Do You Use Coordinates to Translate a Figure Vertically?

    How Do You Use Coordinates to Translate a Figure Vertically?

    Translating a figure on the coordinate plane is easier than you might think! This tutorial shows you how to translate coordinates from the original figure. Then, simply connect the points to create your new figure. This tutorial shows you how!

    • What is a Reflection?What is a Reflection?

    What is a Reflection?

    When you look in the mirror, you see your reflection. In math, you can create mirror images of figures by reflecting them over a given line. This tutorial introduces you to reflections and shows you some examples of reflections. Take a look!

    • What is a Rotation?What is a Rotation?

    What is a Rotation?

    Ever turned a door handle? You were performing a rotation! In math, rotations are just the same! Check out this tutorial to learn about rotations.

    • What is a Translation?What is a Translation?

    What is a Translation?

    Ever slide something across a table? If so, then you have performed a translation! In this tutorial, learn the definition of translation and see some really neat examples. Take a look!

    • What is a Line of Reflection?What is a Line of Reflection?

    What is a Line of Reflection?

    Just about everything in math has a name! Did you know that the line you reflect a figure over has a special name? It's called the line of reflection! Watch this tutorial and learn about the line of reflection.

    • What is a Transformation?What is a Transformation?

    What is a Transformation?

    Transformations can be really fun! They allow you to change or move a figure. In this tutorial, learn about all the different kinds of transformations!

    • What is an Image?What is an Image?

    What is an Image?

    Just about everything in math has a name! Did you know that when you're dealing with transformations, the new figure you get is called an image? Check out this tutorial and learn about this math term!

    • How Can You Tell if a Function is Linear or Nonlinear From a Graph?How Can You Tell if a Function is Linear or Nonlinear From a Graph?
    • How Can You Tell if a Function is Linear or Nonlinear From a Table?How Can You Tell if a Function is Linear or Nonlinear From a Table?

    How Can You Tell if a Function is Linear or Nonlinear From a Table?

    To see if a table of values represents a linear function, check to see if there's a constant rate of change. If there is, you're looking at a linear function! This tutorial shows you how to tell if a table of values represents a linear function.