Question

Examine the graph of f(x) and the table that contains values of g(x).Which function has a greater average rate of change over the interval 0≤x≤1?

Answer 1

Let's determine the rate of change of the two functions at 0 ≤ x ≤ 1.

For f(x),

Point 1: 0, -4

Point 2: 1, 2

$\text{ Rate of change = slope = }\frac{\text{y}_2\text{ - y}_1}{\text{ x}_2\text{ - x}_1}$$\text{ = }\frac{2\text{ - \lparen-4\rparen}}{1\text{ - 0}}\text{ = }\frac{2\text{ + 4}}{1}\text{ = }\frac{6}{1}$$\text{ Rate of change of f\lparen x\rparen = 6}$

For g(x),

Point 1: 0, 3

Point 2: 1, 9

$\text{ Rate of change = }\frac{9\text{ - 3}}{1\text{ - 0}}\text{ = }\frac{6}{1}$$\text{ Rate of change of g\lparen x\rparen = 6}$

Therefore, both functions has the same average rate of change over this interval.

The answer is CHOICE C.