FREE SAT Interpreting Nonlinear Functions Questions and Answers 3

Question 1

The function f is a rational function defined by f(x) = (x^2 - 4) / (x - 2). The graph of y = f(x) in the xy-plane has a point of discontinuity (a hole). What are the coordinates of this hole?

Accepted Answer

(2, 4)

Answer

(-2, 0)

Answer

(2, 0)

Answer

(-2, -4)

Question 2

The graph of a nonlinear piecewise function is shown, consisting of a parabola and a square root function. Which of the following defines the function for x ≥ 0?

Accepted Answer

f(x) = { -x^2 + 4, if 0 ≤ x < 2; √(x-2), if x ≥ 2 }

Answer

f(x) = { x^2 - 4, if 0 ≤ x < 2; √(x-2), if x ≥ 2 }

Answer

f(x) = { -x^2 + 4, if 0 ≤ x < 2; √(x+2), if x ≥ 2 }

Answer

f(x) = { x^2 - 4, if 0 ≤ x < 2; √(x+2), if x ≥ 2 }

Question 3

The function g(x) = a(x - h)^2 + k represents a parabola. The graph of y = g(x) is a parabola that opens downward and has a vertex at (-3, 5). Which of the following MUST be true?

Accepted Answer

a < 0 and k = 5

Answer

a > 0 and h = -3

Answer

a < 0 and h = 3

Answer

a > 0 and k = -5

Question 4

A scientist models the decay of a radioactive substance with the function N(t) = N₀e^(-λt), where N(t) is the amount of the substance at time t, N₀ is the initial amount, and λ is the decay constant. If the half-life of the substance is 100 years, which equation correctly represents the decay constant λ?

Accepted Answer

λ = ln(2) / 100

Answer

λ = 100 / ln(2)

Answer

λ = e / 100

Answer

λ = -ln(0.5) / 100

Question 5

The graph of y = f(x) is shown, which has a horizontal asymptote at y = 2 and a vertical asymptote at x = -1. Which of the following could be the equation for f(x)?

Accepted Answer

f(x) = (2x - 3) / (x + 1)

Answer

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

Answer

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

Answer

f(x) = (x + 1) / (2x - 4)

Question 6

A population of bacteria is modeled by the function P(t) = 100 * (b)^t, where t is time in hours. The population quadruples every 6 hours. What is the value of b?

Accepted Answer

4^(1/6)

Answer

√2

Answer

6^(1/4)

Answer

4