Unit Quiz
Overview
Test your mastery of functions. This comprehensive quiz covers function basics, linear functions, real-world applications, and common errors.
Quiz Questions
Question 1: If f(x) = 4x - 7, find f(5).
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Answer: 13
f(5) = 4(5) - 7 = 20 - 7 = 13
Question 2: Which of the following is a function? A) {(1,2), (1,3), (2,4)} B) {(1,2), (2,2), (3,2)} C) {(1,2), (3,2), (1,4)}
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Answer: B) {(1,2), (2,2), (3,2)}
In B, each x-value has exactly one y-value. A and C have x=1 mapping to multiple y-values.
Question 3: Find the slope and y-intercept of f(x) = -2x + 9.
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Answer: Slope = -2, y-intercept = 9
In the form f(x) = mx + b, m = -2 and b = 9.
Question 4: If g(x) = x² - 4x, find g(6).
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Answer: 12
g(6) = (6)² - 4(6) = 36 - 24 = 12
Question 5: A plumber charges $60 for a service call plus $45 per hour. Write a function and find the cost for a 3-hour job.
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Answer: C(h) = 45h + 60; 3-hour job costs $195
C(3) = 45(3) + 60 = 135 + 60 = $195
Question 6: If f(x) = 3x + 2, find x when f(x) = 20.
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Answer: x = 6
20 = 3x + 2, 18 = 3x, x = 6
Question 7: Is y = 5 a function? Is it linear?
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Answer: Yes, it is a function. Yes, it is linear (with slope 0).
Every x-value gives y = 5. It's a horizontal line, which is linear with m = 0.
Question 8: Given f(x) = 2x - 1 and g(x) = x + 4, find g(f(3)).
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Answer: 9
First: f(3) = 2(3) - 1 = 5. Then: g(5) = 5 + 4 = 9
Question 9: A car's value decreases by $1,500 per year. If it starts at $24,000, write a function V(t) and find its value after 4 years.
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Answer: V(t) = 24000 - 1500t; After 4 years: $18,000
V(4) = 24000 - 1500(4) = 24000 - 6000 = $18,000
Question 10: The table shows inputs 0, 1, 2, 3 with outputs 3, 7, 11, 15. Write the linear function.
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Answer: f(x) = 4x + 3
The rate of change is constant: 7-3=4, 11-7=4, 15-11=4. Slope = 4. y-intercept = 3 (when x=0). So f(x) = 4x + 3.