Unit 1, Day 2 Practice: Translations
SOL Standard: AFDA.AF.1
Name: ___________________________________
Date: _______________
Worked Example
Describe the translations for the equation $f(x) = (x-3)^2 + 4$
- Horizontal Shift: The $(x-3)$ is inside the parentheses. Since it's the opposite of the sign, this is a shift right 3 units.
- Vertical Shift: The $+4$ at the end is outside the function, which means a shift up 4 units.
Part 1: Describe the Translation(s)
For each equation, describe how it moves from the parent function.
1. $f(x) = x^2 + 5$
2. $f(x) = (x-7)^2$
3. $f(x) = 2^x - 10$
4. $f(x) = (x+1)^2$
5. $f(x) = (x+2)^2 + 8$
6. $f(x) = 2^{(x-4)} - 6$
Part 2: Write the Equation
Write the new equation based on the description.
7. The parent function $f(x)=x^2$ is moved left 3 units.
8. The parent function $f(x)=x$ is moved up 12 units.
9. The parent function $f(x)=2^x$ is moved down 1 unit.
10. The parent function $f(x)=x^2$ is moved right 6 units and up 2 units.
11. The parent function $f(x)=2^x$ is moved left 1 unit and up 5 units.
12. The parent function $f(x)=x$ is moved right 4 units.
Part 3: What's the Equation?
The dotted graph is the parent. Write the equation for the solid graph.
13. Equation for Graph A:
14. Equation for Graph B:
15. Equation for Graph C: