Real math help.
What is an Absolute Value Function?
Note:
An absolute value function is just a function that contains absolute values. This tutorial gives a great introduction to this very useful function!
Background Tutorials
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Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.
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What Does Absolute Value Mean?
In this tutorial you'll see how you can think of absolute value in a very intuitive way. Let us know if you have any questions about it!
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Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
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What's a Real Number?
Real numbers are numbers that can be found on the number line. This includes both the rational and irrational numbers. This tutorial explains real numbers and gives some great examples. Take a look!
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Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
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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!
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Lines are taken to lines, and line segments to line segments of the same length.
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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!
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Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
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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!
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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!
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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.
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Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
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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!
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Further Exploration
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Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
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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.
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