Rate of Changes Quiz (AP PreCalc Unit 1 Day 6)

The average rate of change of the function g on the interval (-1, 3) is positive. Which of the following could be the graph of g?

• (A)

• (B)

• (C)

• (D)

The table gives characteristics of the rates of change of the function f on different intervals. Which of the following is true about f on the interval 2 < x < 3?

• (A) f is increasing, and the graph of f is concave down.

• (B) f is increasing, and the graph of f is concave up.

• (C) f is decreasing, and the graph of f is concave down.

• (D) f is decreasing, and the graph of f is concave up.

The figure shows the graph of a function k for 0 ≤ x ≤ 5. Which of the following statements is true about the function k?

• (A) The rate of change of k is positive and increasing.

• (B) The rate of change of k is positive and decreasing.

• (C) The rate of change of k is negative and increasing.

• (D) The rate of change of k is negative and decreasing.

The table shows values for a function f at selected values of x. Which of the following claim and explanation statements best fit these data?

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

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

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

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

The graph of the function y = g(x) is given below. What can be concluded about the rates of change on the interval 2 < x < 3?

• The rates of change are positive.

• The rates of change are increasing.

• The rates of change are negative.

• The rates of change are decreasing.

The function f is given by f(x) = x^2 + 3x - 5 and has a minimum at x = 1.5. Which of the following describes f?

• For any interval of x, the function always has a positive rate of change.

• For any interval of x, the function always has a negative rate of change.

• For any interval of x < 1.5, the function has a positive rate of change, and for any interval of x > 1.5 the function has a negative rate of change.

• For any interval of x < 1.5, the function has a negative rate of change, and for any interval of x > 1.5 the function has a positive rate of change.

The figure shows the graph of a function k in the xy-plane with three labeled points. It is known that a relative maximum of k occurs at B. Consider the rates of change of k at the three labeled points. Which of the following orders the rates of change of k in order from least to greatest?

• A, B, C

• B, A, C

• C, A, B

• C, B, A

Selected values of a function are shown in the table below. Which of the following statements is true of the rates of change?

• The rates of change are negative and increasing.

• The rates of change are negative and decreasing.

• The rates of change are positive and increasing.

• The rates of change are positive and decreasing.

For the polynomial function g, the rate of change of g is increasing for x < 2 and decreasing for x > 2. Which of the following must be true?

• The graph of g has a minimum at x = 2.

• The graph of g has a maximum at x = 2.

• The graph of g has a point of inflection at x = 2, is concave down for x < 2, and is concave up for x > 2.

• The graph of g has a point of inflection at x = 2, is concave up for x < 2, and is concave down for x > 2.

The graph of the function f is given for -3 < x < 6. Which of the following statements about the rate of change of f over the interval -3 < x < 2 is true?

• The rate of change is positive.

• The rate of change is negative.

• The rate of change is increasing.

• The rate of change is decreasing.