Question 9
Examine the graph of f(x)
f
(
x
)
and the table that contains values of g(x).
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).
© 2018 StrongMind. Created using GeoGebra.
x
x
g(x)
g
(
x
)
−1
−
1
1
1
0
0
3
3
1
1
9
9
2
2
27
27
3
3
81
81
Which function has a greater average rate of change over the interval 0≤x≤1?
0
≤
x
≤
1
?
The function f(x)
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)
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. , ,
Both functions have the same average rate of change over this interval.
This is an example of why some questions go unanswered.
The horrible text formatting just makes the eyes bleed.
\Many times, copy/paste from formatted screen shots does not translate well. Unfortunately, this is not clearly explained when students post their questions and attempt to include text from Word documents or other such data.
So, after you have posted, take a look at your submission to make sure it looks the way you want it to.
I cant read it well
Well, it seems like both f(x) and g(x) are on their own race to see who has the greater average rate of change. It's a real nail-biter! But, there can only be one winner. So, after carefully analyzing the situation, I must say that the function f(x) has a greater average rate of change over the interval 0≤x≤1. It's just a tad speedier than g(x). Sorry g(x), better luck next time!
To determine which function has a greater average rate of change over the interval 0 ≤ x ≤ 1, we can calculate the average rate of change for both functions.
For the function f(x), we can use the formula:
Average rate of change = (f(1) - f(0))/(1 - 0)
From the given information, we know that f(0) = -4 and f(1) = 2. Plugging these values into the formula:
Average rate of change for f(x) = (2 - (-4))/(1 - 0) = 6/1 = 6
Now let's calculate the average rate of change for the function g(x). Since the table contains values of g(x), we can look at the change in g(x) over the interval 0 ≤ x ≤ 1.
g(0) = 3 and g(1) = 9. Using the same formula as before:
Average rate of change for g(x) = (9 - 3)/(1 - 0) = 6/1 = 6
Therefore, both functions f(x) and g(x) have the same average rate of change over the interval 0 ≤ x ≤ 1.
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 f(x) over an interval [a, b] is calculated by finding the difference between the function values at the endpoints divided by the difference in the x-values:
Average Rate of Change = (f(b) - f(a)) / (b - a)
Let's calculate the average rate of change for both functions:
For function f(x):
f(1) - f(0) = 2 - (-4) = 6
1 - 0 = 1
Average Rate of Change = 6 / 1 = 6
For function g(x):
g(1) - g(0) = 9 - 3 = 6
1 - 0 = 1
Average Rate of Change = 6 / 1 = 6
Both functions have the same average rate of change over the interval 0 ≤ x ≤ 1. Therefore, the correct answer is:
Both functions have the same average rate of change over this interval.