Question

This table shows the output values of two functions, p(x) and q(x), for specific input values of x.
x p(x)=x−−√−5
q(x)=5x−1−−−−√3
0 −5
−5
1 −4
0
9 −2
10
Compare the estimated average rates of change for the functions p(x)=x−−√−5
and q(x)=5x−1−−−−√3
over the interval [0.1,8.9]
.

(1 point)

The estimated average rates of change of p(x)
and q(x)
are both 13
over [0.1,8.9]
.

The estimated average rates of change of p(x)
and q(x)
are both 53
over [0.1,8.9]
.

The estimated average rate of change of q(x)
is less than the estimated average rate of change of p(x)
over [0.1,8.9]
.

The estimated average rate of change of q(x)
is greater than the estimated average rate of change of p(x)
over [0.1,8.9]
.

Answer 1

q(x) has the greater estimated average rate of change.

Using the table values at x ≈ 0 and x ≈ 9 to approximate the interval [0.1, 8.9]:
- p: (p(9) − p(0)) / (9 − 0) = (−2 − (−5)) / 9 = 3/9 = 1/3
- q: (q(9) − q(0)) / (9 − 0) = (10 − (−5)) / 9 = 15/9 = 5/3

So the average rate for q is greater than for p.