AP Precalculus Unit 1: Test Review

The polynomial function p is given by p(x) = (x + 2)¹. Which of the following expressions is equivalent to (x + 2)² ?

• x² + 2x³ + 4x² + 8x + 16

• x² + 4x³ + 6x² + 4x + 1

• x¹ +8x³ + 24x² + 32x + 16

• 2x¹ +8x³ + 12x² + 8x + 2

Tags

CCSS.HSA.APR.C.5

The graph of the polynomial function g is shown. The function f is defined for 0 ≤ x ≤ 3 and is identical to the function g on that interval. How many total local minima and local maxima does the function f have?

• Two

• Four

• Five

• Seven

A polynomial function p is given by p(x) = − x(x − 4)(x + 2). What are all intervals on which p(x) ≥ 0 ?

• [2,4]

• [2,0] U [4, ∞)

• (-∞, -4] U [0,2]

• (-∞, -2] U [0,4]

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.11

The polynomial function P is given by P(x) = 3x(x + 1)²(x − a), where a is a real number. Which of the following could be the graph of y = P(x) ?

• 
• 
• 
• 

Tags

CCSS.HSA.APR.B.3

For a polynomial function ƒ, lim f(x) = ∞ and lim f(x) = about f?

• The degree of f is even, and the leading coefficient is negative.

• The degree of f is even, and the leading coefficient is positive.

• The degree of f is odd, and the leading coefficient is negative.

• The degree of f is odd, and the leading coefficient is positive.

The function f is given by f(x) -2x7 +5x² + 6x² – 3. Which of the following correctly describes the end behavior of f as the input values increase without bound?

• lim f(x) = ∞

• lim f(x) = -∞

• lim f(x) = ∞

• lim f(x) =10

Tags

CCSS.HSA.APR.A.1

The graph of which of the following functions in the xy-plane has at least one x-intercept, at least one hole, at least one vertical asymptote, and a horizontal asymptote?

Tags

CCSS.HSF-IF.C.7D

The polynomial function f is given by f(x) = 2x³ – 3x² – 23x + 12. Which of the following is true about f(x) ?

• The remainder of is 0. The quotient of f(x) is a quadratic polynomial that factors into two linear factors involving only real numbers.

• The remainder of is 0. The quotient of f(x) is a quadratic polynomial that does not factor into linear factors involving only real numbers.

• The remainder of is a nonzero constant. The quotient of is a quadratic polynomial that factors into two linear factors involving only real numbers.

• The remainder of is a nonzero constant. The quotient of is a quadratic polynomial that does not factor into linear factors involving only real numbers.

Tags

CCSS.HSA.APR.B.2

The functions g and ƒ are given by g(x) = 3x² · 2x and ƒ(x) = 6x¹ + 5x³ + 3x − 5. Which of the following statements is true about the remainder when f(x) is divided by g(x) ?

• The remainder is 0, so g(x) is a factor of f(x).

• The remainder is 0, so f(x) is a factor of g(x).

• The remainder is (7x – 5), so g(x) is not a factor of f(x), and the graph of y has a slant asymptote.

• The remainder is (7x – 5), so g(x) is not a factor of f(x), and the graph of y does not have a slant asymptote.

Tags

CCSS.HSA.APR.B.2

The function ƒ is given by f(x) = 3x² + 2x + 1. The graph of which of the following functions is the image of the graph of f after a vertical dilation of the graph of f by a factor of 2 ?

Tags

CCSS.HSF.BF.B.3