MPT College Algebra 5

Question 1

A polynomial function has zeros at x = -2, x = 0, and x = 5. Which could be its equation?

Accepted Answer

f(x) = x(x + 2)(x - 5)

Answer

Zeros at -2, 0, 5 correspond to factors (x+2), x, and (x-5).

Question 2

Which transformation maps y = x² to y = (x - 2)² + 3?

Accepted Answer

Shift right 2 and up 3

Answer

Replacing x with (x-2) shifts right 2; adding 3 outside shifts up 3.

Question 3

What is the value of the expression 27^(2/3)?

Accepted Answer

9

Answer

27^(2/3) = (27^(1/3))² = 3² = 9.

Question 4

Solve for x: (x + 2)/(x - 1) = 3

Accepted Answer

5/2

Answer

Cross multiply: x + 2 = 3(x - 1) → x + 2 = 3x - 3 → 5 = 2x → x = 5/2.

Question 5

An exponential function f(x) = ab^x passes through (0, 4) and (2, 36). What is b?

Accepted Answer

3

Answer

f(0) = a = 4; f(2) = 4b² = 36 → b² = 9 → b = 3.

(MPT) UCF Math Placement Test Practice Test