College Math Placement Test College Algebra 4

Question 1

Which of the following represents a one-to-one function?

Accepted Answer

f(x) = x³

Answer

f(x) = x³ is strictly increasing, so each output corresponds to exactly one input, making it one-to-one.

Question 2

What is the remainder when x⁴ - 3x² + 2 is divided by (x - 1)?

Accepted Answer

0

Answer

By the Remainder Theorem, substitute x=1: 1 - 3 + 2 = 0, so the remainder is 0.

Question 3

Simplify: (2i)(3 - 4i) where i = √(-1)

Accepted Answer

8 + 6i

Answer

(2i)(3-4i) = 6i - 8i² = 6i + 8 = 8 + 6i, since i² = -1.

Question 4

What is the horizontal asymptote of f(x) = (3x² + 2) / (x² - 5)?

Accepted Answer

y = 3

Answer

When degrees are equal, the horizontal asymptote is the ratio of leading coefficients: y = 3/1 = 3.

Question 5

Solve: 2^(x+1) = 5^x

Accepted Answer

x = ln(2)/(ln(5) - ln(2))

Answer

Taking ln: (x+1)ln2 = x·ln5, so x·ln2 + ln2 = x·ln5, giving x = ln2/(ln5 - ln2).

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