Question

Shown here is the graph of a function f.

Suppose g(x) = −x2 + 10.

Select the function that has the smaller rate of change over the interval [1, 3].

A) f
B) g
C) They are the same.
D) Insufficient information.

Answer 1

Answer: C

Explanation:

I got it right

Answer 2

C) They are the same.

Explanation:

The function f(x) has points as per graph:

• f(1) = 9
• f(3) = 1

So the points are:

• (1, 9) and (3, 1)

Rate of change for f(x):

• (1-9)/(3-1) = - 8/2 = -4

The function g(x) has points:

• g(1) = -1² + 10 = 9
• g(3) = -3² + 10 = 1

So the points are:

• (1, 9) and (3, 1)

Rate of change for f(x):

• (1-9)/(3-1) = - 8/2 = -4

As we see both functions have same rate of change over the interval [1, 3]

The answer choice is: C) They are the same