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.

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;

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;

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

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

The slope of the graph is constant, therefore;

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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:

Where,

a = 1.5, f(a) = 1,

b = 3, f(b) = 4

Plug in the values:

✔️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.

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.

congruent segments

step-by-step explanation: