Question

Lesson 11 function analysis unit test

Answer 1

Sure! It looks like you're preparing for a unit test on functions and possibly function analysis. While I don’t have specific test questions for "Lesson 11," I can help you with a general outline of topics that might be covered in a unit test on function analysis, along with examples and practice questions. Here’s a sample study guide:

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### Function Analysis Unit Test Study Guide

#### Key Topics to Review:

1. **Understanding Functions:**
- Definition of a function
- Domain and range
- Vertical line test

2. **Function Notation:**
- Using f(x) notation
- Evaluating functions
- Example: If f(x) = 2x + 3, what is f(4)?

3. **Types of Functions:**
- Linear functions
- Quadratic functions
- Polynomial functions
- Rational functions
- Exponential and logarithmic functions
- Trigonometric functions

4. **Transformations of Functions:**
- Shifts: vertical and horizontal
- Reflections: over the x-axis and y-axis
- Stretches and compressions

5. **Composition of Functions:**
- Definition and notation
- Example: If f(x) = x^2 and g(x) = x + 1, find (f o g)(x).

6. **Inverse Functions:**
- Definition of inverse functions
- Finding the inverse of a function
- Example: Find the inverse of f(x) = 2x + 3.

7. **Graphing Functions:**
- Key features: intercepts, asymptotes, etc.
- Analyzing the graph of a function
- Symmetry: even and odd functions

8. **Applications of Functions:**
- Word problems involving functions
- Using functions to model real-life situations

### Sample Questions:

1. **Evaluate the Function:**
If \( h(x) = 3x^2 - 5x + 2 \), what is \( h(2) \)?

2. **Identify the Domain:**
What is the domain of the function \( f(x) = \frac{1}{x - 3} \)?

3. **Find the Inverse:**
Find the inverse of the function \( f(x) = 3x - 7 \).

4. **Graphing:**
Sketch the graph of the function \( g(x) = x^2 - 4x + 3 \) and identify the vertex and x-intercepts.

5. **Composition:**
If \( f(x) = x + 2 \) and \( g(x) = x^2 \), find \( (f \circ g)(x) \).

6. **Properties of Functions:**
Determine whether the function \( f(x) = x^3 - 2x \) is even, odd, or neither.

7. **Word Problem:**
A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write a function to describe the total cost \( C \) as a function of miles driven \( m \), and calculate the cost for 100 miles.

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Make sure to practice problem-solving in each of these areas, and review any examples or homework from your lessons that relate to these topics. Good luck with your unit test! If you need more specific questions or explanations on any topic, feel free to ask!