1. 4.6.1 – Absolute Value Functions

2. We now know how to solve and graph different types of inequalities and equations, including those with absolute value Recall, a function will be written in the notation f(x) – What is f? – What is x?

3. Absolute Value Functions A function f(x) = a |x| is considered an absolute value function May plug in any real number of x All function values f(x) ≥ 0 – Why?

4. Symmetric The function f(x) = |x| appears like a “V” Symmetric with the y-axis Each x value is “mirrored” In other words, f(-x) = f(x) Example. f(2) = 2. And, f(-2) = 2.

5. To evaluate an absolute value function, we will do the same as we have with other functions Substitute the given value for every x, then use order of operations PEMDAS – Absolute value is same as “parenthesis”

6. Example. Evaluate the following function when x = 1 and x = -4. f(x) = 2|x + 1|

7. Example. Evaluate the following function when x = 1 and x = -4. f(x) =-3|x – 4| - 3

8. Example. Evaluate the following function when x = 1 and x = -4. f(x) = (1/2) |x + 1|

9. Symmetric Points Sometimes, we may be asked to identify and choose points that are symmetric to a given point Think about the opposite x-value for the symmetric value

10. Example. Find the point of the function f(x) = 8 |x| that is symmetric to the given point (1, 8). What is given x-value?

11. Example. Find the point of the function f(x) = 4|x| + 1that is symmetric to the given point (4, 17) What is given x-value?

12. Assignment Pg. 207 3-5, 11-17 odd, 19, 20, 32, 34