The purpose of this activity is to examine the family of absolute value functions in the form =||+, where a, b, and c are parameters.

1. (4 points) Enter the function 1=|| into your calculator and describe what you see. Please reference concepts of domain, range, and symmetry for full credit. Click or tap here to enter text.

2. (4 points) Now enter the function 1=3|| into your calculator and describe what you see. Make sure to indicate whether it vertically or horizontally stretched or shrunk for credit. Click or tap here to enter text.

3. (4 points) Now enter the function 1=0.5|| into your calculator and describe what you see. Make sure to indicate whether it vertically or horizontally stretched or shrunk for credit. Click or tap here to enter text.

4. (5 points) Now enter the function 1=5|| into your calculator and describe what you see. Make sure to indicate whether it vertically or horizontally stretched or shrunk for credit, and which axis it reflects on. Click or tap here to enter text.

5. (12 points) How does changing the a parameter change your function, 1=||? Check the correct boxes for each situation.

When a>1 the graph will: Vertical Stretch Vertical Shrink Horizontal Stretch Horizontal Shrink Reflects over x-axis Reflects over y-axis

When 0

When a<-1 the graph will: Vertical Stretch Vertical Shrink Horizontal Stretch Horizontal Shrink Reflects over x-axis Reflects over y-axis

When 0>a>-1 the graph will: Vertical Stretch Vertical Shrink Horizontal Stretch Horizontal Shrink Reflects over x-axis Reflects over y-axis

6. (4 points) Now enter the function 1=|| and 2=|+2| into your calculator and describe what you see. Make sure to indicate whether 2 vertically or horizontally moved left or right for credit. Click or tap here to enter text.

7. (4 points) Now enter the function 1=|| and 2=|3| into your calculator and describe what you see. Make sure to indicate whether 2 vertically or horizontally moved left or right for credit. Click or tap here to enter text.

8. (4 points) How does changing the c parameter change your function, 1=||? Check the correct boxes for each situation.

When c>0 the graph will shift: Vertically Right Vertically Left Horizontally Left Horizontally Right

When c<0 the graph will shift: Vertically Right Vertically Left Horizontally Left Horizontally Right

9. (2 points) Now enter the function 1=|| and 2=||+7 into your calculator and describe what you see. Make sure to indicate whether 2 vertically or horizontally moved up or down for credit. Click or tap here to enter text.

10. (2 points) Now enter the function 1=|| and 2=||6 into your calculator and describe what you see. Make sure to indicate whether 2 vertically or horizontally moved up or down for credit. Click or tap here to enter text.

11. (4 points) How does changing the b parameter change your function, 1=||+? Check the correct boxes for each situation.

When b>0 the graph will shift: Vertically Up Vertically Down Horizontally Up Horizontally Down

When b<0 the graph will shift: Vertically Up Vertically Down Horizontally Up Horizontally Down

12. (9 points) Now describe the following function, make sure that you include a detailed description of the shifts and reflections: =6|3|+7 Click or tap here to enter text.

13. (9 points) Now describe the following function, make sure that you include a detailed description of the shifts and reflections: =0.25|+2|3 Click or tap here to enter text.

14. (9 points) Now describe the following function, make sure that you include a detailed description of the shifts and reflections: =|7|2