1. Lesson 2-3: Piecewise and Absolute Value Functions
Advanced Math Topics

2. Piecewise functions Domain Range
A function defined by two or more equations
Each equation applies to a different part of the domain
Domain
it is usually described in the problem and can just be rewritten for the answer
Range
found by taking the endpoints (if there are any) for the domain intervals and plugging them into the appropriate function to find the y-values

3. Summary f(x)= different things for different sections of the graph
Remember what open dots and closed dots mean??

4. Piece Wise Functions
Step 1 Graph the linear function f(x) = –1 for x ≤ 3. Since 3 satisfies this inequality, begin with a closed circle at (3, 2).

5. Step 2. Graph the constant function f(x) = –1 for x > 3
Step 2 Graph the constant function f(x) = –1 for x > 3. Since x does not satisfy this inequality, begin with an open circle at (3, –1) and draw a horizontal ray to the right.

6. Answer: The function is defined for all values of x, so the domain is all real numbers. The values that are y-coordinates of points on the graph are all real numbers less than or equal to 2, so the range is {y | y ≤ 2}.

7. A. B. C. D.

8. Absolute Value Function
A function with a variable inside the absolute value bars
The graph makes a “V” shape

9. To Graph
Take everything inside the | | and set it equal to 0. The x-value you get is the x-value for the corner.
Plug the x-value in and solve for y
The resulting ordered pair is where you absolute value graph starts! (the corner)
Plug in two x-values on either side of the corner to find ordered pairs to finish the graph

10. To Find Domain and Range
Domain: ARN there are no restrictions on the x-values you can plug into an absolute value graph
Range: determined from the y-values, y will be > or < the y-value of the corner

11. Summary

12. Absolute Value

13. Graphs

14. Graph f(x) = |x| – 2 and g(x) = |x| + 3 on the same coordinate plane
Graph f(x) = |x| – 2 and g(x) = |x| + 3 on the same coordinate plane. Which answer choice is not true about the pair of graphs?

15. Identify the type of function

16. Identify the type of function

17. Identify the type of function