Determine which function has the greater rate of change in problems 1-3.
(1 point)
X y
-1. 0
0. 2
1. 3
To determine the rate of change of a function, we need to find the slope of the line that passes through any two points on the function. Let's take the first two points of the table and find the slope:
Slope = (change in y) / (change in x) = (2 - 0) / (0 - (-1)) = 2/1 = 2
Now, let's take the second two points of the table and find the slope:
Slope = (change in y) / (change in x) = (3 - 2) / (1 - 0) = 1/1 = 1
Therefore, we can see that the rate of change of the function between (-1, 0) and (0, 2) is greater than the rate of change of the function between (0, 2) and (1, 3).
To determine which function has the greater rate of change, we first need to calculate the rate of change for each function.
For problem 1, the x-values are -1, 0, and 1, and the corresponding y-values are 0, 2, and 3. The rate of change can be calculated as the change in y divided by the change in x.
The rate of change for problem 1 is:
(2 - 0) / (0 - (-1)) = 2 / 1 = 2
Now let's consider problem 2:
X y
-1. 0
0. 1
1. 3
The rate of change for problem 2 is:
(1 - 0) / (0 - (-1)) = 1 / 1 = 1
Finally, problem 3:
X y
-1. 2
0. 3
1. 5
The rate of change for problem 3 is:
(3 - 2) / (0 - (-1)) = 1 / 1 = 1
Comparing the rates of change, we can see that problem 1 has a rate of change of 2, problem 2 has a rate of change of 1, and problem 3 also has a rate of change of 1.
Therefore, the function with the greater rate of change is problem 1.