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.
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)
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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 -
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 -
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 -
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)
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Determine if the following relation is a function:
\( { (1, 2), (2, 3), (1, 4) } \)
Answer: _______________ -
Describe the end behavior of the function \( f(x) = -2x^3 + 5 \).
Answer: _______________
Section 3: Graphing (3 points each)
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Sketch the graph of the function \( f(x) = x^2 - 4 \).
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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)
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For the piecewise function defined as follows, evaluate \( f(-1) \), \( f(2) \), and \( f(5) \): \[ f(x) = \begin{cases} x^2 & \text{if } x < 0 \ 2x + 1 & \text{if } 0 \leq x < 4 \ 5 & \text{if } x \geq 4 \end{cases} \]
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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)
- 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!