Unit 1, Day 1 Worksheet

Unit 1, Day 1 Practice: Parent Functions

SOL Standard: AFDA.AF.1

Name: ___________________________________

Date: _______________

Worked Example

Identify the parent function for the equation $f(x) = x^2 - 5$.

  1. Step 1 (Look at the variable): Find the variable $x$ in the equation.
  2. Step 2 (Check the exponent): Notice that the $x$ is being squared ($x^2$).
  3. Step 3 (Identify): The parent function where $x$ is squared is the Quadratic parent function, $f(x)=x^2$. The $-5$ just shifts it down, but it's still in the quadratic family.

Part 1: Match the Equation to the Name

Write the letter of the correct parent function equation next to its name.

1. Linear _________

2. Quadratic _________

3. Exponential _________

A) $f(x) = 2^x$

B) $f(x) = x$

C) $f(x) = x^2$

Part 2: Identify the Graph Shape

For each parent function name, describe the shape of its graph.

4. Linear:

5. Quadratic:

6. Exponential:

Part 3: Identify the Parent Function Family

For each equation, write the name of the parent function family it belongs to (Linear, Quadratic, or Exponential).

7. $f(x) = x - 8$

8. $f(x) = (x+3)^2$

9. $f(x) = 2^x + 1$

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

11. $f(x) = 3x$

12. $f(x) = 4^x$

Part 4: Application

13. Which parent function graph goes through the point $(0,0)$ and $(1,1)$?

14. Which parent function graph has a vertex (lowest point) at $(0,0)$?

15. If you graph $y=x$, $y=x^2$, and $y=2^x$ in Desmos, which graph grows the fastest on the right side?