College Math Placement Test Functions 4

Question 1

If f(x) = x² - 4 and g(x) = x + 2, what is (f/g)(x) for x ≠ -2?

Accepted Answer

x - 2

Answer

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:

Accepted Answer

y = f(x+3) - 2

Answer

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)?

Accepted Answer

9

Answer

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?

Accepted Answer

f(x) = x^(1/2) + 2

Answer

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)?

Accepted Answer

x = 3

Answer

The vertex occurs when 2x - 6 = 0, so x = 3.

College Math Placement Test Practice Test