College Math Placement Test Functions 4 — Questions and Answers
Question 1: If f(x) = x² - 4 and g(x) = x + 2, what is (f/g)(x) for x ≠ -2?
- x - 2 (Correct answer)
- x + 2
- x² - 4x - 8
- (x+2)(x-2)
Correct answer: x - 2
f(x)/g(x) = (x²-4)/(x+2) = (x+2)(x-2)/(x+2) = x - 2.
Question 2: The graph of y = f(x) is shifted 3 units left and 2 units down. The new equation is:
- y = f(x+3) + 2
- y = f(x-3) - 2
- y = f(x+3) - 2 (Correct answer)
- y = f(x-3) + 2
Correct answer: y = f(x+3) - 2
Shifting left replaces x with (x+3) and shifting down subtracts 2: y = f(x+3) - 2.
Question 3: If f(x) = 2^x, what is the value of f(0) + f(3)?
- 8
- 9 (Correct answer)
- 10
- 11
Correct answer: 9
f(0) = 2⁰ = 1 and f(3) = 2³ = 8, so f(0) + f(3) = 9.
Question 4: Which of the following functions is NOT a polynomial function?
- f(x) = 3x⁴ - x + 7
- f(x) = x^(1/2) + 2 (Correct answer)
- f(x) = -5
- f(x) = x³ - 2x² + 1
Correct answer: f(x) = x^(1/2) + 2
x^(1/2) = √x involves a fractional exponent, so it is not a polynomial function.
Question 5: For f(x) = |2x - 6|, at what value of x does the graph have a corner (vertex)?
- x = 2
- x = 3 (Correct answer)
- x = 6
- x = -3
Correct answer: x = 3
The vertex occurs when 2x - 6 = 0, so x = 3.
Question 6: If a function f is even and f(4) = 7, then f(-4) equals:
- -7
- 7 (Correct answer)
- -4
- Cannot be determined
Correct answer: 7
Even functions satisfy f(-x) = f(x), so f(-4) = f(4) = 7.
Question 7: Which set of ordered pairs does NOT represent a function?
- {(1,2),(3,4),(5,6)}
- {(0,0),(1,1),(2,2)}
- {(1,2),(1,3),(2,4)} (Correct answer)
- {(2,1),(3,1),(4,1)}
Correct answer: {(1,2),(1,3),(2,4)}
In {(1,2),(1,3),(2,4)}, x = 1 maps to two different y-values (2 and 3), violating the definition of a function.
College Math Placement Test Functions 4
If f(x) = x² - 4 and g(x) = x + 2, what is (f/g)(x) for x ≠ -2?