MPT College Algebra 3

Question 1

What is the domain of f(x) = √(2x - 6)?

Accepted Answer

x ≥ 3

Answer

The radicand must be ≥ 0: 2x - 6 ≥ 0 → x ≥ 3.

Question 2

Which equation represents a circle with center (2, -1) and radius 4?

Accepted Answer

(x-2)² + (y+1)² = 16

Answer

Standard form (x-h)² + (y-k)² = r² with h=2, k=-1, r=4 gives (x-2)² + (y+1)² = 16.

Question 3

Solve for x: log₃(x) = 4

Accepted Answer

81

Answer

Converting from log form: x = 3⁴ = 81.

Question 4

Factor completely: 2x² + 7x + 3

Accepted Answer

(2x + 1)(x + 3)

Answer

Check: (2x + 1)(x + 3) = 2x² + 6x + x + 3 = 2x² + 7x + 3.

Question 5

If f(x) = 2x + 1 and g(x) = x², what is (f ∘ g)(3)?

Accepted Answer

19

Answer

(f ∘ g)(3) = f(g(3)) = f(9) = 2(9) + 1 = 19.

(MPT) UCF Math Placement Test Practice Test