ACT Math: Functions 3 — Questions and Answers
Question 1: What is the range of f(x) = x^2 + 4?
- y >= 4 (Correct answer)
- y >= 0
- all real numbers
- y <= 4
Correct answer: y >= 4
Since x^2 is at least 0, the minimum value is 4.
Question 2: If f(x) = 5x and f(a) = 35, what is a?
- 7 (Correct answer)
- 30
- 175
- 5
Correct answer: 7
5a = 35 means a = 7.
Question 3: The function f(x) = 2^x is evaluated at x = 3. What is the result?
- 8 (Correct answer)
- 6
- 9
- 16
Correct answer: 8
2^3 = 8.
Question 4: If f(x) = |x - 4|, what is f(1)?
- 3 (Correct answer)
- -3
- 5
- 1
Correct answer: 3
|1 - 4| = |-3| = 3.
Question 5: Which of these represents a function?
- {(1,2),(2,3),(3,4)} (Correct answer)
- {(1,2),(1,3),(2,4)}
- {(2,1),(2,2),(3,3)}
- {(0,1),(0,2),(0,3)}
Correct answer: {(1,2),(2,3),(3,4)}
Each x-value maps to exactly one y-value only in the first set.
Question 6: If f(x) = x + 2 and g(x) = 3x, what is (g + f)(2)?
- 10 (Correct answer)
- 8
- 6
- 12
Correct answer: 10
f(2) = 4 and g(2) = 6, so the sum is 10.
Question 7: What is the y-intercept of f(x) = 3x - 6?
- -6 (Correct answer)
- 3
- 6
- 2
Correct answer: -6
Setting x = 0 gives f(0) = -6.
ACT Math: Functions 3
What is the range of f(x) = x^2 + 4?