Question

Look at the graph.

On a coordinate plane, a graph increases through (negative 1, 4), levels off at (0, negative 3), and then increases up through (2, 5).

Leslie analyzed the graph to determine if the function it represents is linear or non-linear. First she found three points on the graph to be (–1, –4), (0, -3), and (2, 5). Next, she determined the rate of change between the points (–1, –4) and (0, -3) to be StartFraction negative 3 minus (negative 4) Over 0 minus (negative 1) EndFraction = StartFraction 1 Over 1 EndFraction = 1. and the rate of change between the points (0, -3) and (2, 5) to be StartFraction 5 minus (negative 3) Over 2 minus 0 EndFraction = StartFraction 8 Over 2 EndFraction = 4. Finally, she concluded that since the rate of change is not constant, the function must be linear. Why is Leslie wrong?​

Answer 1

Answer:

Its D

Step-by-step explanation:

Answer 2

Leslie is wrong because her conclusion is wrong. If the rate of change is not constant, then the function cannot be linear.

The correct option is D.

What is a Linear Function?

A function is said to be linear when the rate rate of change is constant for all the points on the graph.

The points of the graph are  (–1, –4), (0, -3), and (2, 5).

The rate of change from  (–1, –4) to  (0, -3) is

(-3 -(-4)) / (0-(-1)) = 1

The rate of change from (0,-3) to (2,5) is

(5+3)/(2-0) = 4

The rate of change is not constant and so the function cannot be linear.

Leslie is wrong because her conclusion is wrong. If the rate of change is not constant, then the function cannot be linear.

The correct option is D.

The missing options are attached with the answer.

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