Pre-Calculus Flashcards

What are the zeros of f(x) = x³ - 4x?

Answer: x = 0, 2, -2

Factoring: x(x² - 4) = x(x-2)(x+2) = 0 gives x = 0, 2, -2.

Which statement about the function y = 1/x is true?

Answer: It has a vertical asymptote at x = 0

y = 1/x is undefined at x = 0 and has a vertical asymptote there.

Convert 3π/4 radians to degrees.

Answer: 135°

Multiplying by 180/π: (3π/4)(180/π) = 3(180)/4 = 540/4 = 135°.

What is the domain of f(x) = √(x - 5)?

Answer: x ≥ 5

The expression under the square root must be non-negative: x - 5 ≥ 0, so x ≥ 5.

Which form represents a polynomial with roots at x = 1 and x = -4?

Answer: (x - 1)(x + 4)

Roots at x = 1 and x = -4 mean factors (x - 1) and (x - (-4)) = (x + 4).

Simplify: log₃(27) - log₃(3)

Answer: 2

log₃(27) = 3 and log₃(3) = 1, so the difference is 3 - 1 = 2.