The rate of change for function f is greater than the rate of change of function g, therefore the statement that correctly compares the two functions on the interval {0, 2} is: D. Both functions are increasing, but function f is increasing faster.
Recall:
- Rate of change of a function can be calculated using the formula: [tex]\frac{f(b) - f(a)}{b - a}[/tex]
Given the interval {0, 2}, let's find the rate of change of each of the function around this interval.
Rate of change on the interval {0, 2} for the graph of function f:
a = 0
b = 2
f(a) = -2
f(b) = 8
Rate of change = [tex]\frac{8 - (-2)}{2 - 0} = \frac{10}{2} = 5[/tex]
Rate of change on the interval {0, 2} for the table of function g:
a = 0
b = 2
f(a) = -8
f(b) = -2
Rate of change = [tex]\frac{-2 -(-8)}{2 - 0} = \frac{6}{2} = 3[/tex]
In conclusion, the rate of change for function f is greater than the rate of change of function g, therefore the statement that correctly compares the two functions on the interval {0, 2} is: D. Both functions are increasing, but function f is increasing faster.
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