The statement that correctly compares the function shown on this graph with the function y=4x + 2 is 'The function shown on the graph has a smaller rate of change, but a higher starting point.'
What is rate of change of a function?
"It is the rate at which one quantity is changing with respect to another quantity."
What is slope-intercept form of a line?
"y = mx + c, where m is the slope and c is the y-intercept"
For given question,
We have been given a function y = 4x + 2
This function represents a line.
Comparing above function with slop-intercept form of the line.
We have slope of the line = 4 and y - intercept = 2
We know that the rate of change of line is given by its slope.
So, the rate of change of given function y = 4x + 2 is 4.
A starting point of a function is the beginning value in a linear function.
The starting point of above function f(x) is 2.
The graph of the line passing through points (-1, 1) and (0, 4)
So using slope formula,
[tex]m1=\frac{4-1}{0-(-1)}\\\\ m1=\frac{3}{1}\\\\ m1=3[/tex]
So, the rate of change of function shown on the graph is 3.
This means, the rate of change of function shown on the graph is smaller than the rate of change of function y = 4x + 2
The equation of the function shown on the graph would be y = 3x + 4
The starting point of function shown on the graph is 4.
This means the starting point of function shown on the graph is higher than the starting point of a function y = 4x + 2
Therefore, the statement that correctly compares the function shown on this graph with the function y=4x + 2 is 'The function shown on the graph has a smaller rate of change, but a higher starting point.'
The correct answer is option (A)
Learn more about the rate of change of function here:
https://brainly.com/question/21335643
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