The graph of a function $$h$$ is shown. Which of the following best describes the behavior of the graph of $$h(x)$$ from point $$P$$ to point $$Q$$ ?

The graph of $$h$$ is decreasing and concave up.

The graph of $$h$$ is increasing and concave up.

The graph of $$h$$ is increasing and concave down.

The graph of $$h$$ is decreasing and concave down.

Suppose that for a cubic function $$f$$ , at $$x=-4$$ the rate of change is positive, at $$x=1$$ , the rate of change is negative, and at $$x=4$$ , the rate of change is positive. Which statement is true about the graph of $$f$$ ?

The graph of $$f$$ has one maximum point on the interval $$(-4,1)$$ and one minimum point on the interval $$(1,4)$$ .

The graph of $$f$$ has two maximum points on the interval $$(-4,\ 4)$$

The graph of $$f$$ has two minimum points on the interval $$(-4,\ 4)$$

The graph of $$f$$ has one minimum point on the interval $$(-4,1)$$ and one maximum point on the interval $$(1,4)$$ .

Selected values of the polynomial $$k$$ are shown in the table. Which of the following claim and explanation statements could be true about $$k(x)$$ ?

The graph of $$k$$ could be concave up because the average rates of change over consecutive equal-length input-value intervals are increasing.

The graph of $$k$$ could be concave up because the average rates of change over consecutive equal-length input-value intervals are positive.

The graph of $$k$$ could be concave down because the average rates of change over consecutive equal-length input-value intervals are decreasing.

The graph of $$k$$ could be concave down because the average rates of change over consecutive equal-length input-value intervals are negative.

The graph of the function $$h$$ is shown. Which of the following statement pairs about $$h$$ is true?

The rate of change of $$h$$ is negative and decreasing.

The rate of change of $$h$$ h is positive and increasing.

The rate of change of $$h$$ is positive and decreasing.

The rate of change of $$h$$ is negative and increasing.

The rational function $$r$$ is given by $$r\left(x\right)=\frac{2x^2-13x+30}{x-3}$$ . Which of the following statements about $$r$$ is correct?

The graph of $$r$$ has a slant asymptote of $$y=2x+9$$ .

The graph of $$r$$ has a horizontal asymptote at $$y=2$$ .

The graph of r $$r$$ has a slant asymptote of $$y=2x+19$$ .

The graph of $$r$$ has a slant asymptote of $$y=2x-7$$ .

The functions $$f$$ and $$g$$ are defined for all real numbers such that $$g(x)=f(2(x+5))$$ . Which of the following sequences of transformations maps the graph of $$f$$ to the graph of $$g$$ in the $$xy$$ -plane?

Horizontal dilation of the graph of $$f$$ by a factor of $$\frac{1}{2}$$ , followed by a horizontal translation of $$f$$ by $$5$$ units to the left.

Horizontal dilation of the graph of $$f$$ by a factor of $$\frac{1}{2}$$ , followed by a horizontal translation of $$f$$ by $$5$$ units to the right.

Horizontal dilation of the graph of $$f$$ by a factor of $$2$$ , followed by a horizontal translation of $$f$$ by $$5$$ units to the right.

Horizontal dilation of the graph of $$f$$ by a factor of $$2$$ , followed by a horizontal translation of $$f$$ by $$5$$ units to the left.

What type of function would be the most appropriate to model the relationship between $$x$$ and $$y$$ for the data set shown in the table above?

A quadratic function is best, because the rate of change is decreasing at a constant rate.

A linear function is best, because the data roughly appear to form a line.

A linear function is best, because the rate of change is constant.

A quadratic function is best, because the points roughly appear to form a curve.

Let $$h$$ be a polynomial function whose graph has a point of inflection at $$x=4$$ . Which of the following statements about $$h$$ must be true?

The graph of the rate of change of $$h$$ has a relative extremum at $$x=4$$ .

The graph of the rate of change of $$h$$ has a zero that will cross the $$x$$ -axis at $$x=4$$ .

The graph of $$h$$ has a relative extremum at $$x=4$$ .

The graph of $$h$$ is tangent to the $$x$$ -axis at $$x=4$$ .

Let $$f$$ be the function given by $$\frac{1}{3}x^4-\frac{3}{4}x^3-\frac{5}{2}x^2+5x$$

$$f$$ has global minima of approximately $$-9.263$$ and $$-1.852$$ .

$$f$$ has a global maximum of approximately $$2.157$$ .

$$f$$ has a global minimum of approximately $$-9.263$$ .

$$f$$ has neither a global minimum nor global maximum.

The table provides values of the function $$f(x)$$ for $$x$$ -values near $$x=3$$ . Which of the following is true for $$f$$ ?

The rate of change of $$f$$ at $$x=3$$ is approximately $$5.2$$ .

The rate of change of $$f$$ at $$x=3$$ is approximately $$15$$ .

The rate of change of $$f$$ at $$x=3$$ is increasing at a rate of approximately $$5.2$$ .

The rate of change of $$f$$ at $$x=3$$ is increasing at a rate of approximately $$25$$ .

AP Precalculus Unit 1 Multiple Choice Questions

Authored by Victoria Kiser

Mathematics

11th Grade

CCSS covered

Used 3+ times

AP Precalculus Unit 1 Multiple Choice Questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

CCSS.HSF.IF.B.4

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following functions has two vertical asymptotes, one horizontal asymptote, and no holes?

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CCSS.HSF-IF.C.7D

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