Question

The values on the x-axis range from negative 4 to 13 in increments of 1. The values on the y-axis range from negative 1 to 5 in increments of 1. The curve passes through the following plotted points: left parenthesis negative 4 comma 0 right parenthesis, left parenthesis negative 3 comma 1 right parenthesis, left parenthesis 0 comma 2 right parenthesis, left parenthesis 5 comma 3 right parenthesis, and left parenthesis 12 comma 4 right parenthesis.

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)

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

The cube 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.
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Answer 1

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

Reason: p(-4)=√0=0, p(-3)=√1=1, so (1−0)/(−3−(−4)) = 1/1 = 1.
Similarly f(-4)=∛0=0, f(-3)=∛1=1, so its average rate is also 1.