Common Assessment

The depth of water, in feet, at a certain place in a lake is modeled by a function W. The graph of y = W(t) is shown for 0 ≤ t ≤ 30, where t is the number of days since the first day of a month. What are all intervals of t on which the depth of water is increasing at a decreasing rate?

• (A) (3, 6) only

• (B) (3, 12)

• (C) (0, 3) and (18, 30) only

• (D) (0, 6) and (18, 30)

Tags

CCSS.HSF.IF.B.4

Which of the following functions has a zero at x = 3 and has a graph in the xy-plane with a vertical asymptote at x = 2 and a hole at x = 1?

• (A) h(x) = (x^2 - 4x + 3) / (x^2 - 3x + 2)

• (B) j(x) = (x^2 - 5x + 6) / (x^2 - 3x + 2)

• (C) k(x) = (x - 3) / (x^2 - 3x + 2)

• (D) m(x) = (x - 3) / (x^2 - 4x + 3)

Tags

CCSS.HSF-IF.C.7D

The polynomial function p is an odd function. If p(3) = -4 is a relative maximum of p, which of the following statements about p(-3) must be true?

• (A) p(-3) = 4 is a relative maximum.

• (B) p(-3) = -4 is a relative maximum.

• (C) p(-3) = 4 is a relative minimum.

• (D) p(-3) = -4 is a relative minimum.

Tags

CCSS.HSA.APR.D.7

The figure shown is the graph of a polynomial function g . Which of the following could be an expression for g(x) ?

• 0.25(x - 5)(x - 1)(x + 8)

• 0.25(x + 5)(x + 1)(x - 8)

• 0.25(x - 5)^2(x - 1)(x + 8)

• 0.25(x + 5)^2(x + 1)(x - 8)

Tags

CCSS.HSA.APR.B.3

The table gives values for a polynomial function f at selected values of x . Let g(x) = af(bx) + c , where a, b, and c are positive constants. In the xy-plane, the graph of g is constructed by applying three transformations to the graph of f in this order: a horizontal dilation by a factor of 2, a vertical dilation by a factor of 3, and a vertical translation by 5 units. What is the value of g(-4) ?

• (A) 266

• (B) 170

• (C) 28

• (D) 20

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.5

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.LE.A.4

Tags

CCSS.HSF.BF.A.2

• -72

• 9

• 97

Tags

CCSS.HSF-BF.A.1C

A food vendor developed a new sandwich type for sale. The vendor made estimates about the sales of the new sandwich type over time. A linear regression was used to develop a model for the sales over time. The figure shows a graph of the residuals of the linear regression. Which of the following statements about the linear regression is true?

• The linear model is not appropriate, because there is a clear pattern in the graph of the residuals.

• The linear model is not appropriate, because the graph of the residuals has more points above 0 than below 0.

• The linear model is appropriate, because there is a clear pattern in the graph of the residuals.

• The linear model is appropriate, because the positive residual farthest from 0 and the negative residual farthest from 0 are about the same distance, although more points are above 0 than below 0.