The correct option is Option C: The function shown on the graph has a greater rate of change and a higher starting point.
What is the rate of change of function?
The rate of change of function is the change in the value of the function with respect to x value.
rate of change of function f(x)= df(x)/dx= f'(x)
Here the function given in the question is y=2x-5
rate of change of function= f'(x)= df(x)/dx= dy/dx= d(2x-5)/dx= 2
the starting point of the function f is y-intercept of the function.
the y-intercept of the function is the point where the function touches the y-axis which can be calculated by putting x value is equals to 0.
y= 2x-5
⇒y= 2*0-5
⇒y= -5
The starting point of function is -5.
Given the graph has slope = |y-intercept| / |x intercept|
= 4/1 =4
rate of change of graph = slope of graph= 4
similarly, the y-intercept of the function is the point where the function touches the y-axis which can be calculated by putting x value is equals to 0.
The y-intercept of the graph= the starting point of the graph= -5
Therefore the function in the graph has a higher rate of change as well as a higher starting point.
From the above, it is clear that the correct option is Option C: The function shown on the graph has a greater rate of change and a higher starting point.
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