Asked by jhgfd
What is the rate of change of the table below?
x 1 2 3 4 5 6
f(x) 12 19 26 33 40 47
Responses
7
7
-12
-12
17
1 seventh
12
x 1 2 3 4 5 6
f(x) 12 19 26 33 40 47
Responses
7
7
-12
-12
17
1 seventh
12
Answers
Answered by
GPT-4 Turbo
To find the rate of change of the function given the values in the table, we look at how the value of f(x) changes as x increases. Let's take the differences between consecutive values of f(x):
For x = 2 and x = 1:
f(2) - f(1) = 19 - 12 = 7
For x = 3 and x = 2:
f(3) - f(2) = 26 - 19 = 7
For x = 4 and x = 3:
f(4) - f(3) = 33 - 26 = 7
For x = 5 and x = 4:
f(5) - f(4) = 40 - 33 = 7
For x = 6 and x = 5:
f(6) - f(5) = 47 - 40 = 7
As we can see, each time x increases by 1, f(x) increases by 7. So the rate of change, also known as the slope for this linear function, is constant at 7.
Therefore, the correct rate of change is 7.
For x = 2 and x = 1:
f(2) - f(1) = 19 - 12 = 7
For x = 3 and x = 2:
f(3) - f(2) = 26 - 19 = 7
For x = 4 and x = 3:
f(4) - f(3) = 33 - 26 = 7
For x = 5 and x = 4:
f(5) - f(4) = 40 - 33 = 7
For x = 6 and x = 5:
f(6) - f(5) = 47 - 40 = 7
As we can see, each time x increases by 1, f(x) increases by 7. So the rate of change, also known as the slope for this linear function, is constant at 7.
Therefore, the correct rate of change is 7.
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