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Functions & their graphs unit test unit 7 lesson 12
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Sure! Here’s a general outline for a unit test on Functions and Their Graphs, specifically tailored for a lesson that might include concepts typically covered in Unit 7, Lesson 12. You can adapt this based on specific topics covered in your curriculum.
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**Unit Test: Functions & Their Graphs**
**Name: ________________________ Date: ________________**
**Instructions:** Answer all questions to the best of your ability. Show your work where necessary.
---
**Section 1: Multiple Choice (1 point each)**
1. Which of the following represents a function?
a) \( y = x^2 + 3 \)
b) \( x^2 + y^2 = 4 \)
c) \( x = 2y + 1 \)
d) None of the above
2. What is the range of the function \( f(x) = \sqrt{x-1} \)?
a) \( x \geq 1 \)
b) \( y \geq 0 \)
c) \( y \leq 0 \)
d) All real numbers
3. The graph of the function \( f(x) = x^3 - 3x \) has:
a) No x-intercepts
b) One x-intercept
c) Two x-intercepts
d) Three x-intercepts
4. Which transformation would shift the graph of \( f(x) = x^2 \) upward by 3 units?
a) \( f(x) = x^2 + 3 \)
b) \( f(x) = x^2 - 3 \)
c) \( f(x) = x^2 \)
d) \( f(x) = 3x^2 \)
---
**Section 2: Short Answer (2 points each)**
5. Determine if the following relation is a function:
\( \{ (1, 2), (2, 3), (1, 4) \} \)
**Answer:** _______________
6. Describe the end behavior of the function \( f(x) = -2x^3 + 5 \).
**Answer:** _______________
---
**Section 3: Graphing (3 points each)**
7. Sketch the graph of the function \( f(x) = x^2 - 4 \).
8. Identify the vertex, axis of symmetry, and intercepts of the quadratic function \( f(x) = 2(x-3)^2 + 1 \).
---
**Section 4: Problem Solving (5 points each)**
9. For the piecewise function defined as follows, evaluate \( f(-1) \), \( f(2) \), and \( f(5) \):
\[
f(x) = \begin{cases}
x^2 & \text{if } x < 0 \\
2x + 1 & \text{if } 0 \leq x < 4 \\
5 & \text{if } x \geq 4
\end{cases}
\]
10. Given the function \( f(x) = -3x + 1 \), determine the equation of the line that is perpendicular to \( f(x) \) and passes through the point (2, 3).
---
**Section 5: Bonus (Extra Credit) (3 points)**
11. Describe how you could determine if two functions are inverses of each other. Provide an example of two functions that are inverses.
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**End of Test**
---
Feel free to modify the test to align more closely with the specific objectives and topics from your lesson!
---
**Unit Test: Functions & Their Graphs**
**Name: ________________________ Date: ________________**
**Instructions:** Answer all questions to the best of your ability. Show your work where necessary.
---
**Section 1: Multiple Choice (1 point each)**
1. Which of the following represents a function?
a) \( y = x^2 + 3 \)
b) \( x^2 + y^2 = 4 \)
c) \( x = 2y + 1 \)
d) None of the above
2. What is the range of the function \( f(x) = \sqrt{x-1} \)?
a) \( x \geq 1 \)
b) \( y \geq 0 \)
c) \( y \leq 0 \)
d) All real numbers
3. The graph of the function \( f(x) = x^3 - 3x \) has:
a) No x-intercepts
b) One x-intercept
c) Two x-intercepts
d) Three x-intercepts
4. Which transformation would shift the graph of \( f(x) = x^2 \) upward by 3 units?
a) \( f(x) = x^2 + 3 \)
b) \( f(x) = x^2 - 3 \)
c) \( f(x) = x^2 \)
d) \( f(x) = 3x^2 \)
---
**Section 2: Short Answer (2 points each)**
5. Determine if the following relation is a function:
\( \{ (1, 2), (2, 3), (1, 4) \} \)
**Answer:** _______________
6. Describe the end behavior of the function \( f(x) = -2x^3 + 5 \).
**Answer:** _______________
---
**Section 3: Graphing (3 points each)**
7. Sketch the graph of the function \( f(x) = x^2 - 4 \).
8. Identify the vertex, axis of symmetry, and intercepts of the quadratic function \( f(x) = 2(x-3)^2 + 1 \).
---
**Section 4: Problem Solving (5 points each)**
9. For the piecewise function defined as follows, evaluate \( f(-1) \), \( f(2) \), and \( f(5) \):
\[
f(x) = \begin{cases}
x^2 & \text{if } x < 0 \\
2x + 1 & \text{if } 0 \leq x < 4 \\
5 & \text{if } x \geq 4
\end{cases}
\]
10. Given the function \( f(x) = -3x + 1 \), determine the equation of the line that is perpendicular to \( f(x) \) and passes through the point (2, 3).
---
**Section 5: Bonus (Extra Credit) (3 points)**
11. Describe how you could determine if two functions are inverses of each other. Provide an example of two functions that are inverses.
---
**End of Test**
---
Feel free to modify the test to align more closely with the specific objectives and topics from your lesson!
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