The table shows values for the function f while the graph shows function g. Which function has the greatest slope

Question

X. Y
1. 4
3. 10
5. 16
7. 22
9. 28

Answer 1

To determine the slope for each function, we need to calculate the change in y divided by the change in x.

For function f:
The change in y is 28 - 4 = 24
The change in x is 9 - 1 = 8
So the slope for function f is 24/8 = 3.

For function g:
Let's use the graph to estimate the change in y and change in x.
From x = 1 to x = 3, the change in y is 10 - 4 = 6
From x = 3 to x = 5, the change in y is 16 - 10 = 6
From x = 5 to x = 7, the change in y is 22 - 16 = 6
From x = 7 to x = 9, the change in y is 28 - 22 = 6

From x = 1 to x = 3, the change in x is 3 - 1 = 2
From x = 3 to x = 5, the change in x is 5 - 3 = 2
From x = 5 to x = 7, the change in x is 7 - 5 = 2
From x = 7 to x = 9, the change in x is 9 - 7 = 2

Since the change in y is the same for each interval and the change in x is also the same for each interval, the slope for function g is constant and equal to the change in y divided by the change in x of any interval. Therefore, the slope for function g is 6/2 = 3.

Both functions have the same slope of 3, so neither one has a greater slope than the other.