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).
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?
A. 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. , ,
B. The function g(x) has a greater average rate of change over this interval.The function g of x has a greater average rate of change over this interval. , ,
C. Both functions have the same average rate of change over this interval.
Well, it seems like both f(x) and g(x) are having a little competition for the greater average rate of change over the interval 0≤x≤1. It's like a race of functions, but with numbers instead of runners!
Now, to determine who takes the lead, let's calculate the average rate of change for both functions.
For f(x), we can use the slope formula, which is (change in y)/(change in x). Let's calculate it using the given points (0, -4) and (1, 2):
(change in y) = 2 - (-4) = 6
(change in x) = 1 - 0 = 1
So, the average rate of change for f(x) over the interval 0≤x≤1 is 6/1 = 6.
Now, let's do the same for g(x) using the values from the table:
(change in y) = 9 - 3 = 6
(change in x) = 1 - 0 = 1
So, the average rate of change for g(x) over the interval 0≤x≤1 is also 6/1 = 6.
Oh boy, it looks like we have a tie! Both f(x) and g(x) have the same average rate of change over the interval 0≤x≤1. So the answer is C: "Both functions have the same average rate of change over this interval."
I hope the functions don't get too upset about being tied. After all, it's all just a numbers game, right?
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 is calculated by finding the difference in y-values divided by the difference in x-values.
For function f(x), we can use the given points (0, -4) and (1, 2) to calculate the average rate of change:
Average rate of change = (change in y) / (change in x) = (2 - (-4)) / (1 - 0) = 6 / 1 = 6
For function g(x), we can use the given points (0, 3) and (1, 9) to calculate the average rate of change:
Average rate of change = (change in y) / (change in x) = (9 - 3) / (1 - 0) = 6 / 1 = 6
Both functions have the same average rate of change over the interval 0≤x≤1. Therefore, the answer is C. Both functions have the same 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.
For function f(x), we can use the formula for average rate of change:
Average rate of change = (f(1) - f(0)) / (1 - 0)
Given that f(0) = -4 and f(1) = 2, we can substitute these values into the formula:
Average rate of change for f(x) = (2 - (-4)) / (1 - 0)
= (2 + 4) / 1
= 6 / 1
= 6
Now let's calculate the average rate of change for function g(x) using the same formula:
Average rate of change = (g(1) - g(0)) / (1 - 0)
Given that g(0) = 3 and g(1) = 9, we can substitute these values into the formula:
Average rate of change for g(x) = (9 - 3) / (1 - 0)
= 6 / 1
= 6
Both functions f(x) and g(x) have the same average rate of change over the interval 0≤x≤1, so the answer is option C.