1. Warm up

2. Absolute Value Function 7.5

3. This is a new function, with its own equation and graph.

4. What is Absolute Value? Absolute value represents the distance a number is from 0. Thus, it is always positive.

5. The symbol |x| represents the absolute value of the number x. Absolute value is denoted by the bars |3|

6. Make it Easy Everything in the bars becomes positive. If it is already positive, it stays the same. If it is negative, it becomes positive. |8| = 8 and |-8| = 8

7. |-9| = 9 |4| = 4 You try: |15| = ? |-23| = ? Examples

8. We can evaluate expressions that contain absolute value symbols. Think of the | | bars as parenthesis. Example: 2 |5-9| = 2 |-4| = 2 |4| = 8

9. Solving Equations Steps 1. Get absolute value alone on one side of equal sign. 2. Drop the bars and set up 2 equations, one positive and one negative. 3. Solve both equations. 4. You will have 2 answers at the end.

10. |x + 2| +7 = 14 Isolate the absolute value expression by subtracting 7. |x + 2| +7 = 14 |x + 2| = 7 Set up two equations to solve. x + 2 = 7 x + 2 = -7 x = 5 or x = -9 Check: 3|x + 2| - 7 = 14 3|x + 2| -7 = 14 3|5 + 2| - 7 = 14 3|-9+ 2| -7 = 14 3|7| - 7 = 14 3|-7| -7 = 14 21 - 7 = 14 21 - 7 = 14 14 = 14 14 = 14

11. Example

13. Now Try These Solve |y + 4| - 3 = 0 |y + 4| = 3 You must first isolate the variable by adding 3 to both sides. ] Write the two separate equations. y + 4 = 3&y + 4 = -3 y = -1 y = -7

14. You try again!