Unit 1, Day 3 Worksheet

Unit 1, Day 3 Practice: Reflections

SOL Standard: AFDA.AF.1

Name: ___________________________________

Date: _______________

Worked Example

Describe the transformations for the equation $f(x) = -(x+5)^2$

  1. Reflection: The negative sign in the very front flips the graph over the x-axis.
  2. Horizontal Shift: The $(x+5)$ inside the parentheses moves the graph left 5 units.

Part 1: Describe the Transformation(s)

For each equation, describe how it is reflected and/or shifted.

1. $f(x) = -x^2$

2. $f(x) = (-x)^2$ (Hint: Graph this one on Desmos! Does it look different?)

3. $f(x) = -2^x$

4. $f(x) = -x+3$

5. $f(x) = -(x-1)^2$

6. $f(x) = (-x+4)^2 - 2$

7. $f(x) = -(x+3)^2 + 5$

8. $f(x) = 2^{-x}$

Part 2: Write the Equation

Write the new equation based on the description.

9. The parent function $f(x)=x^2$ is reflected over the x-axis.

10. The parent function $f(x)=x$ is reflected over the x-axis and moved down 2 units.

11. The parent function $f(x)=2^x$ is reflected over the x-axis and moved left 4 units.

12. The parent function $f(x)=x^2$ is reflected over the y-axis and moved right 3 units.

13. The parent function $f(x)=x^2$ is reflected over the x-axis and moved down 1 unit.

14. The parent function $f(x)=x$ is reflected over the x-axis and moved left 2 units.

Part 3: What's the Equation?

The dotted graph is the parent. Write the equation for the solid graph.

15. Equation for Graph A:

A

16. Equation for Graph B:

B

17. Equation for Graph C:

C