Bluebook SAT Math: Advanced Functions Questions and Answers

Question 1

The function f is defined by f(x) = x^2 - 8x + 15. The graph of y = f(x) in the xy-plane is a parabola. Which of the following is the best interpretation of the vertex of the parabola?

Accepted Answer

The minimum value of f(x) is -1, which occurs at x = 4.

Answer

The minimum value of f(x) is 15, which occurs at x = 0.

Answer

The maximum value of f(x) is 4, which occurs at x = -1.

Answer

The maximum value of f(x) is 15, which occurs at x = 8.

Question 2

A biologist models the population of a certain species of bacteria with the function P(t) = 100(2)^(t/3), where P(t) is the population after t hours. Which of the following equations best models the amount of time, t, in hours, it will take for the population to reach 1,600?

Accepted Answer

1600 = 100(2)^(t/3)

Answer

1600 = 100(2)^(3t)

Answer

100 = 1600(2)^(t/3)

Answer

1600 = 100(t/3)^2

Question 3

If f(x) = 3x + 7 and g(x) = x^2 - 1, what is the value of f(g(3))?

Accepted Answer

31

Answer

256

Answer

16

Answer

8

Question 4

The function h is defined by h(x) = (x-5)^3 + 2. For which of the following values of x is h(x) = 10?

Accepted Answer

7

Answer

-7

Answer

3

Answer

13

Question 5

Which of the following expressions is equivalent to (x^2 - 9)/(x+3) for x ≠ -3?

Accepted Answer

x - 3

Answer

x + 3

Answer

x - 6

Answer

x^2 - 3

Question 6

The graph of the function f(x) = a(x+1)(x-3) is a parabola that passes through the point (1, -8). What is the value of a?

Accepted Answer

2

Answer

-4

Answer

-2

Answer

4