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Which of the following statement(s) describes the rate of change of f over the interval 1.5 ≤ x ≤ 3? Select all that apply.

The graph with the X-coordinate marks 0, 2, and 4. The Y-coordinate mark 0, 2, and 4. There is graph of absolute value function “f” which opens downwards. The function has a vertex at (1, 0). It passes through the points (1.5, 1) and (3, 4).
A. The rate of change is 12.
B. The rate of change is 2.
C. The rate of change is constant.
D. The rate of change is increasing.

Which of the following statements describes the rate of change of f over the interval 15 x 3 Select all that apply The graph with the Xcoordinate marks 0 2 and class=

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akposevictor

Answer:

B. The rate of change is 2.

C. The rate of change is constant.

D. The rate of change is increasing.

Step-by-step explanation:

Rate of change over 1.5 ≤ x ≤ 3:

[tex] rate of change = \frac{f(b) - f(a)}{b - a} [/tex]

Where,

a = 1.5, f(a) = 1,

b = 3, f(b) = 4

Plug in the values:

[tex] rate of change = \frac{4 - 1}{3 - 1.5} = \frac{3}{1.5} = 2 [/tex]

✔️The rate of change = 2

✔️The rate of change is increasing because the value is a positive value.

✔️The rate of change is also constant over 1.5 ≤ x ≤ 3 since the line is straight.

The points on the interval of the absolute value function in the graph are on the same straight line.

The statements that describe the rate of change over the interval; 1.5 ≤ x ≤ 3 are;

  • B. The rate of change is 2
  • C. The rate of change is constant

Reasons:

The given parameter of the graph of the f are;

The vertex of the function = (1, 0)

The straight line of the function f passes through the points (1.5, 1) and (3, 4)

Therefore;

[tex]\displaystyle The \ slope \ of \ the \ graph \ between \ (1.5, \, 1) \ and \ (3, \, 4) = \mathbf{\frac{4 - 1}{3 - 1.5} }= \frac{3}{1.5} =2[/tex]

The slope of the graph = The rate of change of the graph

Therefore;

The rate of change of the graph over the interval 1.5 ≤ x ≤ 3 is 2

  • The rate of change is 2

Given that the graph is a straight line graph, we have;

The slope of the graph is constant, therefore;

  • The rate of change is constant

Learn more about the graph of linear functions here:

https://brainly.com/question/17090820

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