Question

Use the image to answer the question.

A curve labeled p of x and five points on the curve are plotted on a coordinate plane. The curve begins on the x-axis sloping upward from left to right, passes through quadrant 2, and then rises through quadrant 1.
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Compare the average rates of change for the graphed square root function p(x)=x+4−−−−√
and the cube root function f(x)=x+4−−−−√3
over the interval [−4,−3]
.

(1 point)
Responses

The functions have the same average rate of change of 0.
The functions have the same average rate of change of 0.

The cube root function has the greater average rate of change.
The cube root function has the greater average rate of change.

The square root function has the greater average rate of change.
The square root function has the greater average rate of change.

The functions have the same average rate of change of 1.

Answer 1

Average rate of change = [value at -3 − value at -4] / 1.

For p(x)=√(x+4): p(-4)=0, p(-3)=√1=1, so average = (1−0)/1 = 1.
For f(x)=∛(x+4): f(-4)=0, f(-3)=∛1=1, so average = (1−0)/1 = 1.

So the functions have the same average rate of change of 1.