Question
The table below represents a linear function. Identify the rate of change of the function.
xx yy
minus, 4−4 minus, 1−1
minus, 2−2 00
00 11
22 22
xx yy
minus, 4−4 minus, 1−1
minus, 2−2 00
00 11
22 22
Answers
GPT 3.5
The rate of change of a linear function is the amount by which the function's output (y-value) changes for every 1 unit increase in the input (x-value).
From the given table:
- The function's output remains constant at -4 for input values of -4 and -1. Hence, its rate of change is 0 for this interval.
- The function's output changes from -4 to 0 when the input changes from -4 to 0. So, for a 4 unit increase in the input, the output increases by 4 units. Hence, the rate of change is 1 for this interval.
- The function's output remains the same when the input changes from 0 to 2. Therefore, the rate of change is 0 for this interval as well.
Overall, the rate of change of the function is:
0 for x-values between -4 and -1
1 for x-values between -4 and 0
0 for x-values between 0 and 2
From the given table:
- The function's output remains constant at -4 for input values of -4 and -1. Hence, its rate of change is 0 for this interval.
- The function's output changes from -4 to 0 when the input changes from -4 to 0. So, for a 4 unit increase in the input, the output increases by 4 units. Hence, the rate of change is 1 for this interval.
- The function's output remains the same when the input changes from 0 to 2. Therefore, the rate of change is 0 for this interval as well.
Overall, the rate of change of the function is:
0 for x-values between -4 and -1
1 for x-values between -4 and 0
0 for x-values between 0 and 2
What is the rate of change of the function y, equals, 5x, plus, 4y=5x+4?
GPT 3.5
In the equation y = 5x + 4, we can see that the coefficient of x is 5. This means that for every 1 unit increase in x, the value of y will increase by 5 units.
Therefore, the rate of change of the function y = 5x + 4 is 5.
Therefore, the rate of change of the function y = 5x + 4 is 5.