Unit Exam 3
9 of 169 of 16 Questions
Question
Examine the graph of f(x) and the table that contains values of g(x).
Curve f of x approaches Y equals negative 7 on the left and positive infinity on the right. It passes through points (0, negative 4) and (1, 2).
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x g(x)
−1 1
0 3
1 9
2 27
3 81
Which function has a greater average rate of change over the interval 0≤x≤1?
Both functions have the same average rate of change over this interval.Both functions have the same average rate of change over this interval. , ,
The function f(x) has a greater average rate of change over this interval.The function f of x has a greater average rate of change over this interval. , ,
The function g(x) has a greater average rate of change over this interval.
To determine which function has a greater average rate of change over the interval 0 ≤ x ≤ 1, we need to calculate the average rate of change for both functions.
The average rate of change of a function over an interval is given by the formula:
Average rate of change = (change in y) / (change in x)
For function f(x), we can calculate the average rate of change between x = 0 and x = 1 using the given points:
Change in y = 2 - (-4) = 6
Change in x = 1 - 0 = 1
Average rate of change for f(x) = (6) / (1) = 6
For function g(x), we can calculate the average rate of change between x = 0 and x = 1 using the given points:
Change in y = 9 - 3 = 6
Change in x = 1 - 0 = 1
Average rate of change for g(x) = (6) / (1) = 6
Since both functions have the same average rate of change of 6 over the interval 0 ≤ x ≤ 1, the correct answer is:
Both functions have the same average rate of change over this interval.