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Advanced Functions Introduction

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Advanced Functions Introduction

📚 Part 1: Function Types and Notation

1. Which equation represents a quadratic function?

f(x) = 3x + 7

f(x) = 2x² - 5x + 1

f(x) = 4 · 3ˣ

f(x) = 8

2. If f(x) = 2ˣ, what is f(3)?

6

8

9

23

3. Which characteristics apply to exponential functions? (Check all that apply)

Contains a variable in the exponent

Graph is always a straight line

Shows rapid growth or decay

Has the form f(x) = a · bˣ

4. Given g(x) = -x² + 4, find g(-2).
5. Match each function type with its typical graph shape:

Linear function: ________________

Quadratic function: ________________

Exponential function: ________________

Word bank: parabola, straight line, curved growth/decay

✏️ Part 2: Domain, Range, and Analysis

6. Define a function in your own words. What makes a relation a function?
7. For the function h(x) = 5x - 3:

a) What is the domain? ________________

b) Calculate h(0) = ________________

c) Calculate h(4) = ________________

d) This is a ________________ function.

8. A savings account starts with $100 and earns 5% interest each year. The function A(t) = 100(1.05)ᵗ represents the account balance after t years.

a) What type of function is this? ________________

b) How much money is in the account after 2 years? Show your work:

c) What does the number 1.05 represent in this context?

📊 Part 3: Graphing and Interpretation

9. Consider the quadratic function f(x) = x² - 4x + 3.

a) Complete the table of values:

x = 0: f(0) = ____

x = 1: f(1) = ____

x = 2: f(2) = ____

x = 3: f(3) = ____

x = 4: f(4) = ____

b) Based on your calculations, what is the minimum value of this function? ________________

10. Sketch a rough graph of each function type in the space below:

Label each graph as linear, quadratic, or exponential

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