Bluebook SAT Math: Advanced Functions Questions and Answers 2

Question 1

The function f(x) is an even function and the function g(x) is an odd function. Which of the following describes the function h(x) = 2f(x) - f(x)g(x)?

Accepted Answer

Neither even nor odd

Answer

Even

Answer

Odd

Answer

Both even and odd

Question 2

The function f(x) = x^3 - x^2 - 4x + 4 has three distinct real roots. A new function is defined as g(x) = |f(x)|. How many local minima does the graph of y = g(x) have?

Accepted Answer

Three

Answer

One

Answer

Two

Answer

Four

Question 3

Let f(x) = √(x - 3) and g(x) = x^2 + 2. What is the domain of the composite function h(x) = f(g(x))?

Accepted Answer

x ≥ 1 or x ≤ -1

Answer

x ≥ 3

Answer

x ≥ √3

Answer

All real numbers

Question 4

A rational function is given by f(x) = (ax^2 + 5x - 2) / (3x^2 - bx - 12). If the function has a vertical asymptote at x = -3/2 and a horizontal asymptote at y = 2, what is the value of b?

Accepted Answer

-4

Answer

2

Answer

-2

Answer

4

Question 5

A polynomial P(x) has real coefficients. The graph of y=P(x) has x-intercepts at x=2 and x=-1. If 3 - i is also a root of P(x)=0, what is the lowest possible degree of P(x)?

Accepted Answer

4

Answer

3

Answer

5

Answer

6

Question 6

The temperature, T, in degrees Celsius, of a chemical reaction after t minutes is modeled by the function T(t) = A(0.85)^(t/k) + 18. The initial temperature of the reaction is 168°C, and A, k are positive constants. The model indicates that the temperature will eventually cool to the surrounding room temperature. What does the value of k represent in this context?

Accepted Answer

The time, in minutes, it takes for the temperature difference between the reaction and the room to be reduced to 85% of its current value.

Answer

The final temperature of the reaction.

Answer

The time it takes for the initial temperature difference to decrease by 15%.

Answer

The initial temperature difference between the reaction and the room.