The graph represents function 1, and the equation represents function 2:
Function 1
A coordinate plane graph is shown. A horizontal line is graphed passing through the y-axis at y = 4.
Function 2
y = 8x + 12
How much more is the rate of change of function 2 than the rate of change of function 1? (4 points)
3
4
5
8
HELP PLEASE!
Please!
function 2
dy/dx = slope = 8
function 1
slope= 0
difference = 8
To compare the rates of change of the two functions, let's first calculate the rate of change for each function.
The rate of change is the slope of a function and can be found using the formula:
rate of change = (change in y) / (change in x)
For Function 1:
Since it is a horizontal line passing through the y-axis at y = 4, the line is parallel to the x-axis, meaning the change in y is 0 for any change in x. Therefore, the rate of change for Function 1 is 0.
For Function 2:
The given equation is y = 8x + 12. This is in slope-intercept form (y = mx + b), where m represents the slope. Thus, the rate of change for Function 2 is 8.
Now, to find how much more the rate of change of Function 2 is than the rate of change of Function 1, we subtract the rate of change of Function 1 from the rate of change of Function 2:
8 - 0 = 8
Therefore, the rate of change of Function 2 is 8 units more than the rate of change of Function 1.