Unit 1, Day 3 Practice: Reflections
SOL Standard: AFDA.AF.1
Name: ___________________________________
Date: _______________
Worked Example
Describe the transformations for the equation $f(x) = -(x+5)^2$
- Reflection: The negative sign in the very front flips the graph over the x-axis.
- 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:
16. Equation for Graph B:
17. Equation for Graph C: