Question

Madison created two functions.

For Function A,

The table below represents Function B.
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Function B​

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3


​In comparing the rates of change, which statement about Function A and Function B is true?
A
Function A and Function B have the same rate of change.
B
Function A has a greater rate of change than Function B has.
C
Function A and Function B both have negative rates of change.
D
Function A has a negative rate of change and Function B has a positive rate of change.

SHOW HINT

Answer 1

Function A has a negative rate of change and is steeper than Function B, which has a positive rate of change, making Option D correct.

Step-by-step explanation:

Given the various descriptions of Function A and Function B, we can determine that Function A is a decreasing line while Function B is an increasing line. Taking into account the steepness of the lines, we can deduce that Function A is steeper than Function B.

Therefore, we can declare that the correct statement is Option D: Function A has a negative rate of change and Function B has a positive rate of change. This is because a steeper decreasing line suggests a greater but negative rate of change, and an increasing line denotes a positive rate of change.

In the context of functions, the rate of change refers to how much the output (y-value) changes for a given change in the input (x-value). In this case, since Function A has a steeper slope or a greater inclination than Function B, it means that the rate of change for Function A is greater than that of Function B. Therefore, option B is the correct statement.