High School: Functions

More Specific Topics in High School: Functions

Popular Tutorials in High School: Functions

How Do You Write an Equation for a Translation of an Absolute Value Function?

Want to write an equation to translate the graph of an absolute value equation? This tutorial takes you through that process step-by-step! Take an absolute value equation and perform a vertical and horizontal translation to create a new equation. Watch it all in this tutorial.
How Do You Graph an Absolute Value Function?

Graphing an absolute value equation can be complicated, unless you know how to dissect the equation to find and use the slope and translations. Follow along as this tutorial shows you how to identify the necessary parts of the equation and use them to graph the absolute value equation.
What Does the Constant 'k' do in y = |x|+k?

When you're learning about translating absolute value equations, learning about vertical translations is a MUST! Check out this tutorial and see what it takes to translate an absolute value equation vertically.
What Does the Constant 'h' do in y = |x-h|?

When you're learning about translating absolute value equations, learning about horizontal translations is a MUST! Check out this tutorial and see what it takes to translate an absolute value equation horizontally.
What is an Absolute Value Function?

An absolute value function is just a function that contains absolute values. This tutorial gives a great introduction to this very useful function!
How Do You Graph an Exponential Function Using a Table?

Graphing an exponential function? No sweat! Create a table of values to give you ordered pairs. Then, plot those ordered pair on a coordinate plane and connect the points to make your graph! Follow along with this tutorial as it shows you all the steps.
How Do You Identify Exponential Behavior from a Pattern in the Data?

Take a look at how you identify exponential behavior from a pattern in your data. You'll also see how to figure out if that pattern represents exponential growth or exponential decay. Check it out!
How Do You Solve a Word Problem with Exponential Growth?

If something increases at a constant rate, you may have exponential growth on your hands. In this tutorial, learn how to turn a word problem into an exponential growth function. Then, solve the function and get the answer!
How Do You Solve a Word Problem with Exponential Decay?

If something decreases in value at a constant rate, you may have exponential decay on your hands. In this tutorial, learn how to turn a word problem into an exponential decay function. Then, solve the function and get the answer!
How Do You Write a Rule for a Geometric Sequence?

Trying to find the value of a certain term in a geometric sequence? Use the formula for finding the nth term in a geometric sequence to write a rule. Then use that rule to find the value of each term you want! This tutorial takes you through it step-by-step.
How Do You Solve a Word Problem Using an Exponential Function?

Word problems let you see math in the real world! This tutorial shows you how to create a table and identify a pattern from the word problem. Then you can see how to create an exponential function from the data and solve the function to get your answer!
What Does the Value of 'a' Do in the Exponential Function f(x)= a (bx)?

Multiplying an exponential function by a constant changes the function's graph. Watch the tutorial to find out how!
What's an Exponential Function?

Looking at an equation with a variable in the exponent? You have an exponential function! Learn about exponential functions in this tutorial.
What is Exponential Growth?

Exponential functions often involve the rate of increase or decrease of something. When it's a rate of increase, you have an exponential growth function! Check out these kinds of exponential functions in this tutorial!
What is exponential decay?

Exponential functions often involve the rate of increase or decrease of something. When it's a rate of decrease, you have an exponential decay function! Check out these kinds of exponential functions in this tutorial!
What is the Explicit Formula for the nth Term in a Geometric Sequence?

Trying to find the value of a certain term in a geometric 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 a geometric sequence! This tutorial shows you how find that formula!
How Do You Graph a Rational Function by Making a Table?

Graphing a rational function can be fun, especially when you make a table of values first! In this tutorial, you'll see how to make a table of ordered pairs that you can use to graph the rational function. Take a look!
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 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?
How Do You Write an Equation of a Line in Slope-Intercept Form If You Have Two Points?

Trying to write an equation in slope-intercept form? Have two points on your line? You'll need to find your slope and y-intercept. Watch this tutorial and see what needs to be done to write an equation in slope-intercept form!
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?

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?

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!
How Do You Write an Equation for Direct Variation Given a Point?

Looking for some practice with direct variation? Watch this tutorial, and get that practice! This tutorial shows you how to take given information and turn it into a direct variation equation. Then, see how to use that equation to find the value of one of the variables.
How Do You Write an Equation for Direct Variation from a Table?

Looking for some practice with direct variation? Watch this tutorial, and get that practice! This tutorial shows you how to take a table of values and describe the relation using a direct variation equation.
How Do You Graph a Vertical Line?

To graph a vertical line that goes through a given point, first plot that point. Then draw a straight line up and down that goes through the point, and you're done! To see this process in action, watch this tutorial!
How Do You Graph a Horizontal Line?

To graph a horizontal line that goes through a given point, first plot that point. Then draw a straight line left and right that goes through the point, and you're done! To see this process in action, watch this tutorial!
How Do You Use X- and Y-Intercepts To Graph a Line In Standard Form?

To find the x-intercept of a given linear equation, simply remove the 'y' and solve for 'x'. To find the y-intercept, remove the 'x' and solve for 'y'. In this tutorial, you'll see how to find the x-intercept and the y-intercept for a given linear equation. Check it out!
How Do You Graph a Line If You're Given the Slope and the Intercept?

Trying to graph a line from a given slope and y-intercept? Think you need to find an equation first? Think again! In this tutorial, see how to use that given slope and y-intercept to graph the line.
How Do You Write an Equation of a Line in Point-Slope Form If You Have the Slope and One Point?

Trying to write an equation in point-slope form? Got a point on the line and the slope? Plug those values correctly into the point-slope form of a line and you'll have your answer! Watch this tutorial to get all the details!
How Do You Write an Equation of a Line in Point-Slope Form If You Have Two Points?

Trying to write an equation in point-slope form? Have two points but no slope? You'll need to use those points to find a slope first. Watch this tutorial and see what needs to be done to write an equation in point-slope form!
How Do You Write an Equation of a Line in Point-Slope Form and Standard Form If You Have Two Points?

Get some practice with the point-slope form and standard form of an equation! This tutorial shows you how to use two given points to write an equation in both forms. Take a look!
How Do You Write an Equation of a Line in Slope-Intercept Form If You Have the Slope and the Y-Intercept?

Want to write an equation in slope-intercept form? Already have the slope and y-intercept? Perfect! Just correctly plug those values into your equation and you're done! Learn how in this tutorial.
What's the X-Intercept?

When you have a linear equation, the x-intercept is the point where the graph of the line crosses the x-axis. In this tutorial, learn about the x-intercept. Check it out!
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?

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.
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!
What's the Y-Intercept?

When you have a linear equation, the y-intercept is the point where the graph of the line crosses the y-axis. In this tutorial, learn about the y-intercept. Check it out!
How Do You Find the Zeros of a Quadratic Function on a Graph?

The zeros of a quadratic equation are the points where the graph of the quadratic equation crosses the x-axis. In this tutorial, you'll see how to use the graph of a quadratic equation to find the zeros of the equation. Take a look!
How Do You Solve a Quadratic Equation by Factoring?

One of the many ways you can solve a quadratic equation is by factoring it. In this tutorial, you'll see how to factor a quadratic equation using the guess and check method of factoring. Then, use the zero product property to find the solution!
How Do You Solve a Quadratic Equation by Completing the Square?

One of the many ways you can solve a quadratic equation is by completing the square. In this method, you want to turn one side of the equation into a perfect square trinomial. This tutorial takes you through the steps of solving a quadratic equation by completing the square. Check it out!
How Do You Graph a Quadratic Function?

When you're trying to graph a quadratic equation, making a table of values can be really helpful. Before you make a table, first find the vertex of the quadratic equation. That way, you can pick values on either side to see what the graph does on either side of the vertex. Watch this tutorial to see how you can graph a quadratic equation!
How Do You Determine if the Vertex Will Be a Maximum or Minimum?

The vertex of a quadratic equation is either a maximum or a minimum of the function. But how do you tell if it will be a maximum or a minimum? Watch this tutorial and find the answer to that question!
How Do You Determine if a Graph Represents a Linear, Exponential, or Quadratic Function?

Graphs come in all sorts of shapes and sizes. In algebra, there are 3 basic types of graphs you'll see most often: linear, quadratic, and exponential. Check out this tutorial and learn how to determine is a graph represents a linear, quadratic, or exponential function!
What is the Vertex of a Quadratic Function?

Each quadratic equation has either a maximum or minimum, but did you that this point has a special name? In a quadratic equation, this point is called the vertex! Take a look at the vertex of a quadratic equation by watching this tutorial.
What is the Maximum of a Quadratic Function?

When you're dealing with quadratic functions, maximum and minimum are very likely to come up. This tutorial takes a look at the maximum of a quadratic function. Check it out!
What is the Minimum of a Quadratic Function?

When you're dealing with quadratic functions, maximum and minimum are very likely to come up. This tutorial takes a look at the minimum of a quadratic function. Check it out!
What is a Quadratic Function?

You can't go through algebra without seeing quadratic functions. The graphs of quadratic functions are parabolas; they tend to look like a smile or a frown. In this tutorial, get introduced to quadratic functions, look at their graphs, and see some examples of quadratic functions!
How Do You Graph a Square Root Function Using a Table?

Making a table of values is a useful way to graph a square root function. Just remember to choose x-values for which the function is defined! Watch the tutorial to find out more.
What Does the Constant 'k' Do in the Function f(x)=[square root of](x)+k?

When you're learning about translating square root functions, learning about vertical translations is a MUST! Check out this tutorial and see what it takes to translate a square root function vertically.
How Do You Horizontally Translate a Square Root Function?

When you're learning about translating square root functions, learning about horizontal translations is a MUST! Check out this tutorial and see what it takes to translate a square root function horizontally.
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 Use the Formula for Direct Variation?

If two things are directly proportional, you can bet that you'll need to use the formula for direct variation to solve! In this tutorial, you'll see how to use the formula for direct variation to find the constant of variation and then solve for your answer.
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?

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 Graph a Linear Equation 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 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 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 the Range of a Relation?

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 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 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.
How Do You Graph a Piecewise Function?

If you want to graph a piecewise linear function, graph each function on it's specific interval separately. Bring it all together, and you have your graph! This tutorial shows you the entire process for graphing a piecewise linear function.
How Do You Translate a Function?

Think about sliding a penny on a table. All you're doing is moving the penny to a new location on the table. That's basically all that's happening when you translate a function! When you translate a function, you're just sliding it to a new location on the coordinate plane!
How Do You Graph a Translation of a Function?

A great way to better understand how to translate a function is to practice! This tutorial takes you through the steps of graphing a function that's been translated up and to the right.
How Do You Reflect a Function?

When you look in the mirror, you see a reflection of yourself. Reflections in math involve flipping something over a line called the line of reflection. This tutorial shows you how to reflect a function over a chosen line!
How Do You Find f(x) When the Value for x Contains Other Variables?

When you're evaluating a function, you're usually given a number to plug in for the variable, but what if the expression you're plugging in contains other variables? See how to plug an expression with variables into a function! This tutorial will show you!
How Do You Graph a Reflection of a Function?

If you change a function like f(x) to f(-x), it flips the function over the y-axis! Follow along with this tutorial to see how to take a function and reflect it over the y-axis.
What is the Parent Function of a Cubic Function?

The graph of a linear function is a line. The graph of a quadratic function is a parabola. What does the graph of a cubic function look like? This tutorial introduces you to the basic (parent) function for cubic functions!
How Do You Solve a Quadratic Equation with Complex Solutions by Completing the Square?

You can solve a quadratic equation by completing the square! This tutorial shows you the steps needed to solve a quadratic using this method.
How Do You Convert a Quadratic from Standard Form to Vertex Form by Completing the Square?

The vertex form of a quadratic equation can help you quickly identify the vertex of that quadratic. Follow along with this tutorial to see how to use the completing the square method to change a quadratic equation from standard form to vertex form!
How Do You Convert a Quadratic from Standard Form to Vertex Form by Completing the Square if a≠1?

You can change a quadratic equation from standard form to vertex form by completing the square! This tutorial takes you through the process step-by-step.
How Do You Graph a Quadratic Equation in Intercept Form?

Graphing a quadratic equation in intercept form is a breeze! All the information you need is in the equation. You just need to pick it out and use it. Follow along with this tutorial to see how to take an equation intercept form and use it to find the x-intercepts, vertex, and axis of symmetry.
How Do You Graph a Polynomial Function by Making a Table?

How could you graph a complicated polynomial function? By making a table of course! In this tutorial, you'll see how a table is made and used to graph a higher order polynomial function.
How Do You Translate a Polynomial Function Vertically?

Translating functions can be fun when you know what to do. This tutorial helps you practice translating a function and writing the new function and graph!
How Do You Find the Sum of Two Functions?

Adding functions is easier than you might think! Follow along with this tutorial to learn how to add two functions together.
What are Function Operations?
How Do You Evaluate a Logarithm?

If you want to solve a logarithm, you can rewrite it in exponential form and solve it that way! Follow along with this tutorial to practice solving a logarithm by first converting it to exponential form.
How Do You Convert From Logarithmic Form to Exponential Form?

Rewriting a logarithm in exponential form can make solving easier. In this tutorial, you'll see how to take a logarithm and rewrite it in exponential form!
How Do You Convert From Exponential Form to Logarithmic Form?

Having a problem in exponential form is great, but can you change it to logarithmic form? This tutorial shows you that process step-by-step!
How Do You Simplify Logarithms Using the Product Property?

If you're adding logarithms that have the same base, you can use the Product Property of Logarithms to make that job easier! Follow along with this tutorial to see how the Product Property of Logarithms is used to add logarithms with the same base.
How Do You Convert From Exponential Form to Natural Logarithmic Form?

Converting from exponential form to natural logarithmic form is easier than you might think! Follow along with this tutorial to see how to perform this conversion.
How Do You Convert From Natural Logarithmic Form to Exponential Form?

Rewriting a natural logarithm in exponential form can make solving easier. This tutorial shows you how to take a natural logarithm and convert it to exponential form!
What Does the Constant 'k' Do to the Graph of f(x)=log(x)+k?

Translating a logarithmic function vertically can be fun, especially when you know how it's done! This tutorial shows what it takes to shift a logarithmic function up and down!
How Do You Graph the Natural Base Exponential Function?

Want to graph a natural base exponential function? Make a table of points! Then plot the points, connect them, and you have your graph! Follow along with this tutorial to see the entire process step-by-step.
How Do You Solve a Logarithmic Equation by Exponentiating?

Equations involving logarithms don't have to be scary. Just get rid of the logarithm by exponentiating and solve like any other equation! This tutorial shows you all the steps.
What is a Logarithm?

Logarithms can be tricky, but they become a whole lot easier if you understand how they're related to exponents. Follow along with the tutorial to learn about this relationship.
What is a Natural Logarithm?

A natural logarithm is a logarithm that has a special base. In this tutorial, you'll be introduced to natural logarithms!
What is e?

In math, 'e' isn't just a letter, it's an irrational number! This tutorial shows you how mathematicians use the letter 'e' to represent a specific value and how having a base of 'e' is called a natural base.
What is the Natural Base Exponential Function?

The natural base exponential function is actually a function that's shorter than its name! This tutorial introduces you to this special function and shows you what it looks like.
What is an Angle in Standard Position?

Understanding how angles are made in the coordinate plane is a big step towards understanding trigonometry. This tutorial shows you how an angle can be made in the coordinate plane!
What Does the Graph of the Sine Function Look Like?
What Does the Graph of the Cosine Function Look Like?

You can use the unit circle to help you graph the cosine function! In this tutorial, you'll learn how to do exactly that!
What Does the Graph of the Tangent Function Look Like?

If you want to make the graph of the tangent function, you can use the unit circle to help you plot points. This tutorial shows you how to use the unit circle to make the tangent function graph!
What is a Periodic Function?

Periodic functions have some special qualities! In this tutorial, you'll be introduced to these functions and learn what a graph must have to be called a periodic function.
How Do You Horizontally Translate a Trigonometric Graph?

Translating a graph of sine or cosine horizontally can be fun, but you need to understand how it works. Follow along with this tutorial to learn how to horizontally shift the sine and cosine graphs!
How Do You Use the Formula for Compound Interest?

If you already have a bank account or if you plan to have one in the future, then this tutorial is a must see! Follow along as this tutorial goes through a word problem involving compound interest.
What is the Formula for Compound Interest?

Things like bank accounts, loans, investments, and mortgages are a part of life, and almost always, interest is involved. Sometimes, you need to deal with compound interest, so it would be good to know the formula for it! In this tutorial, you'll see the formula for compound interest. Take a look!
How Do You Find the Rate of Change Between Two Points on a Graph?

The rate of change is a rate that describes how one quantity changes in relation to another quantity. In this tutorial, practice finding the rate of change using a graph. Check it out!
How Do You Find the Rate of Change Between Two Points in a Table?

The rate of change is a rate that describes how one quantity changes in relation to another quantity. This tutorial shows you how to use the information given in a table to find the rate of change between the values in the table. Take a look!
How Do You Write the Equation of a Line in Slope-Intercept Form If You Have a Graph?

Working with the graph of a line? Trying to find the equation for that graph? Just pick two points on the line and use them to find the equation. This tutorial shows you how to take two points on the graph of a line and use them to find the slope-intercept form of the line!
How Do You Write the Equation of a Line in Slope-Intercept Form If You Have a Table?

Looking at a table of values that represents a linear equation? Want to find that equation? Then check out this tutorial! You'll see how to use values from a table to find the slope-intercept form of the line described in the table.
How Do You Use Point-Slope Form to Write an Equation from a Table?

Looking at a table of values that represents a linear equation? Want to find that equation? Then check out this tutorial! You'll see how to use values from a table and the point-slope form of a line to find the slope-intercept form of the line described in the table.
What is Rate of Change?

Trying to describe the how something changes in relation to something else? Use rate of change! In this tutorial, learn about rate of change and see the difference between positive and negative rates of change!