Unit 1 AP Precalculus Practice Test 2025

Let c(x) represent a fourth-degree polynomial function with real coefficients. When y = c(x) is graphed, it is found that c(5) = 3 and c(9) = 4. Which statement must be true?

Which of the following are functions?

I. y − x = 17 + 2x
II. x2 + y² = 64
III. x − y² = 81
IV. x2 + y = 4

If the function f is defined by f(x) = 3x + k and the function g is defined by g(x) = \frac{x - 1} {3} , for what value of k is f(g(x)) = g(f(x))?

If f(x) = x² + 1, then f(a − 1) =

As a pot of boiling water cools, the temperature of the water is recorded and placed in the table below, where time t is measured in minutes and temperature F(t) is measured in degrees Fahrenheit. Using the data in the table, which of the following best approximates the rate at which the temperature of the water is changing at time t = 3.5?

For what value of k is (x + 1) a factor of the function g(x) = x⁴ + 6x³ + k x² − 26x − 24?

Three of the roots of a polynomial equation with rational coefficients are −3, 2i, and −4 + 5 √6 . What is the lowest possible degree of the equation?

Which of the following is the end behavior asymptote for the function

f(x) \frac{x^{3} - 8} {x^{2} 3x - 4}?

Let f be a polynomial function that is even and continuous on the closed interval [−3, 3]. The function f has the properties indicated in the table below.

Which of the following could be a graph of f?

If the graph of  y = \frac{ax + b} {x + c}   has a horizontal asymptote y = 2 and a vertical asymptote x = −3, what is the sum of a and c?

For the function f(x) = x² − 4x + 1, evaluate f(x + h).

Let f(x) represent a third-degree polynomial function with real coefficients. When y = f(x) is graphed, it is found that f(3) = −1 and f(4) = 2. Which statement must be true?

Which of the following functions has a domain of x > 0?

Cailey wants to buy a new outdoor heater. The cost for the unit is $349.99. If she plans to run the heater 5 months out of the year for an annual operating cost of $121.67, which function models the cost per year over the lifetime of the unit, C(t), in terms of the number of years, t, that she owns the heater?

(C) c(t) = \frac{349.99 + 121.67t} {t} .

Which of the following linear functions are increasing?

Find the average rate of change of f(x) = 3 x² − 2 from x = 2 to x = 6

Based on the accompanying graph of the polynomial function y = h (x), which statement must be true?

The accompanying graph represents the equation of the polynomial function y = f(x).

Which graph represents g(x) if g(x) = −f(x) + 3?

Which of the following equations could represent the graph shown below?

Given the nonconstant polynomial function f(x) whose domain is [a, e] where a < b < c < d < e, if f(b) = f(c) = f(d) = 0 and no other values of x in the domain are such that f(x) = 0, which statement must be true?

A rare species of insect was discovered on a tropical island. To protect the species, scientists moved the insects to a protected area. The population P of the insect t months after being moved is  p(t) = \frac{50 (l + 0.5t)} {(2+0.01t} .  How many insects were initially discovered?

A ball is thrown into the air such that its height, h, in feet at any time, t, in seconds is given by the function h(t) = −16t² + 80t + 10. What is the maximum height attained by the ball?

Given the table of values below, which of the following best describes the behavior of the graph of the function in the interval 1 ≤ x ≤ 6?

If a represents the zero of the function f(x) = (x − 3)², evaluate g(a) if g(t) = 10 − 2 (t − 1)³.

Cailey loves to bake and decides to open her own cookie stand, named Cailey’s Cookies. Her daily fixed costs are $120 a day, and each cookie costs $0.99 to bake. Which of the following represents a model that expresses the cost, C, of baking m cookies in a day?