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Parent Functions Worksheet

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Parent Functions Worksheet worksheet preview

Parent Functions Worksheet

Mathematical functions and graphs illustration

📚 Part 1: Identifying Parent Functions

1. Which parent function is represented by the equation y = x²?

Linear

Quadratic

Cubic

Square Root

2. The equation y = |x| represents which type of function?

Absolute Value

Exponential

Reciprocal

Linear

3. Which of the following are characteristics of the linear parent function y = x? (Check all that apply)

Domain: all real numbers

Range: all real numbers

Has a vertex

Passes through the origin

4. The exponential parent function y = 2^x has which domain and range?

Domain: all real numbers, Range: all real numbers

Domain: all real numbers, Range: y > 0

Domain: x ≥ 0, Range: y ≥ 0

Domain: x > 0, Range: all real numbers

✏️ Part 2: Function Analysis

5. For the reciprocal function y = 1/x, what happens to the graph as x approaches 0?
6. Complete the table for parent function characteristics:

Linear function y = x has y-intercept at _______ and x-intercept at _______.

Quadratic function y = x² has vertex at _______ and opens _______.

Square root function y = √x has domain _______ and range _______.

7. Explain how you can identify a cubic function by looking at its equation. Give an example.
8. Show your work to find the domain and range of y = √x:

🌍 Part 3: Real-World Applications

9. Match each real-world situation with the most appropriate parent function type:

A ball thrown in the air (height vs. time): _________________

Population growth over time: _________________

Distance traveled at constant speed: _________________

The relationship between pressure and volume of a gas: _________________

10. Choose one parent function and describe a real-life situation where it might be used. Explain why this function type fits the situation.

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