This week in PreCalc 11 we learned how to graph absolute value functions.

Absolute Value Functions is a function that contains an algebraic expression within absolute value symbols. When we learned about Absolute Values before, we learned that whatever number is between the absolute value symbols must come out a positive. For example, | -3 | = 3 . Absolute Value Functions are similar in the sense that the y-values for Absolute Value Functions must be equal to or greater than zero.

Example:

y = | -5x + 10 |

Step 1: Graph the Parent Function

The first step to graphing this Absolute Value Function is to graph the parent function. The parent function is the same function but without the absolute value symbols. In this case, the parent function is y = -5x + 10.

Step 2: Move the Negative Y-Values

As I mentioned before, y-values in the parent function can’t be less than zero which is where the absolute value function comes in. As I mentioned earlier, | -3 | equals 3 because they’re both the same distance from zero on the number line. This relates back to absolute value functions because the negative y-values for the parent function, when put in the absolute value symbols, is a positive. So all we have to do is change the negative y-values into a positive and then graph it again.

That is how you graph Absolute Value Functions