Unit 1 Worksheet

Unit 1 Practice: Function Families & Transformations

SOL Standard: AFDA.AF.1

Name: ___________________________________

Date: _______________

Worked Example

Describe all transformations for the equation $f(x) = - (x+2)^2 + 3$

  1. Identify the Parent Function: Because of the $x^2$, the parent function is Quadratic.
  2. Horizontal Shift: The $(x+2)$ is inside the parentheses. This means a shift left 2 units (opposite of the sign).
  3. Reflection: The negative sign in front is outside the function, which means a reflection (flip) over the x-axis.
  4. Vertical Shift: The $+3$ at the end is outside the function, which means a shift up 3 units.

Part 1: Identify the Parent Function

For each equation, write whether it belongs to the Linear, Quadratic, or Exponential family.

1. $f(x) = 3x - 5$

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

3. $f(x) = 5^x + 1$

4. $f(x) = -x^2 - 8$

5. $f(x) = 4(2^x)$

6. $f(x) = \frac{1}{2}x + 10$

Part 2: Describe the Transformations

For each equation, list all the transformations from its parent function.

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

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

9. $f(x) = 3(x+1)$

10. $f(x) = 4x^2 - 3$

11. $f(x) = -(x+6)$

12. $f(x) = \frac{1}{2}(x-1)^2 + 5$

Part 3: Write the Equation from the Graph

Look at the graph. Identify the parent function, describe the shift(s), and write the final equation.

13. Equation for Graph A:

A

14. Equation for Graph B:

B

15. Equation for Graph C:

C

Part 4: Challenge

16. Write the equation for a linear function that has been stretched by a factor of 2 and moved up 1 unit.

17. Look at the equation $f(x) = x^2 - 5$. Where is its vertex (the bottom of the 'U') compared to the parent function? Explain how you know.