Selected values of the polynomial k are shown in the table above. Which of the following Claim and explanation statements could be true about k(x)? (A) The graph of k could be concave up because the average rates of change over consecutive equal-length input-value intervals are positive. (B) The graph of k could be concave up because the average rates of change over consecutive equal-length input-value intervals are increasing. (C) The graph of k could be concave down because the average rates of change over consecutive equal-length input-value intervals are decreasing. (D) 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 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 up because the average rates of change over consecutive equal-length input-value intervals are positive.

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 down because the average rates of change over consecutive equal-length input-value intervals are negative.

The graph of the function h(x) is shown above. Which of the following statement pairs about h is true?

The rate of change of h is negative and increasing.

The rate of change of h is positive and increasing.

The rate of change of h is positive and decreasing.

The rate of change of h is negative and decreasing.

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

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

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

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

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

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?

B. 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.

A. 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.

C. 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.

D. 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 f(x) = $$\frac{1}{3}x^4 - \frac{3}{4}x^3 - \frac{5}{2}x^2 + 5x$$ .

f has a global minimum of approximately −9.263

f has a global maximum of approximately 2.157

f has global minima of approximately −9.263 and −1.852

f has neither a global minimum nor global maximum.

The table above 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 15.

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

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 Non Calculator Multiple Choice Questions

Authored by Howard Martin

Mathematics

10th Grade

CCSS covered

Used 9+ times

AP Precalculus Unit 1 Non Calculator Multiple Choice Questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The graph of f(x) is shown above. On which of the following open intervals is the graph of f decreasing at an increasing rate?

0 < x < 1

0 < x < 2

1 < x < 2

x > 1

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The table gives certain values of the function g(x). On which of the following intervals is the average rate of change of g the greatest?

[0,3]

[0,6]

[3,6]

[6,10]

The graph of a function h is shown in the figure above. 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 increasing and concave up.

The graph of h is increasing and concave down.

The graph of h is decreasing and concave up.

The graph of h is decreasing and concave down.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the average rate of change of g over the interval 0 ≤ x ≤ 5?

3/10

2/5

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 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 maximum point on the interval (-4, 1) and one minimum point on the interval (1, 4).

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A salesperson for Euler Industries earns a commission of $400 for the first 10,000 of sales and then $200 for each additional $10,000 or partial of sales. Let S(x) represent the commission earned for x dollars of sales. What is S(75,000)?

$1,500

$1,600

$1,800

$3,200

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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AP Precalculus Unit 1 Non Calculator Multiple Choice Questions

The graph of f(x) is shown above. On which of the following open intervals is the graph of f decreasing at an increasing rate?

The table gives certain values of the function g(x). On which of the following intervals is the average rate of change of g the greatest?

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

What is the average rate of change of g over the interval 0 ≤ x ≤ 5?

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?

A salesperson for Euler Industries earns a commission of $400 for the first 10,000 of sales and then $200 for each additional $10,000 or partial of sales. Let S(x) represent the commission earned for x dollars of sales. What is S(75,000)?

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

Suppose that the point (2, 4) is on the graph of y = j(x). Find a point on the graph of the given function with the given transformation of y = j(x + 2) + 2.

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