The table shows values for the function f while the graph shows function g. Which function has the greatest slope
X. Y
1. 4
3. 10
5. 16
7. 22
9. 28
To determine the slope of a function, we need to find the change in y-values divided by the change in x-values.
For function f:
Change in y = 10 - 4 = 6
Change in x = 3 - 1 = 2
Slope of f = Change in y / Change in x = 6 / 2 = 3
Now, we need to analyze the graph for function g to find its slope. Since there is no information provided for the graph, we cannot determine the slope of function g.
Therefore, function f has the greatest slope, which is 3.
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.
To determine the function with the greatest slope, we need to compare the differences in the y-values (vertical change) and x-values (horizontal change) for each function. The slope of a function is defined as the ratio of the vertical change to the horizontal change.
To find the slope of function f, we can choose any two points, say (1, 4) and (9, 28), and use the slope formula: slope = (y2 - y1)/(x2 - x1).
Using (1, 4) and (9, 28) for function f:
slope = (28 - 4)/(9 - 1) = 24/8 = 3
To find the slope of function g from the graph, we can choose any two points on the line and calculate the slope using the same formula.
Since we don't have the graph of function g, we can't determine the exact values of the points or calculate the slope in this scenario. However, if you have access to the graph of function g, you can choose any two points on the graph and apply the slope formula to determine the slope.
Comparing the slopes calculated for function f and the one you found for function g, the function with the greatest slope can be determined.