The statement that correctly compares the function shown on the 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?
The rate at which one quantity is changing with respect to another quantity.
For given question;
It is given a function y = 4x + 2
This function represents a line.
We have slope of the line = 4 and y - intercept = 2
We already 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.
The starting point of function f(x) is 2.
The graph of the line passing through points (-1, 1) and (0, 4)
So using slope formula,
m = (4-1)/ 0-(-1)
m = 3
So, the rate of change of function is 3.
The rate of change of function shown on the graph is smaller than the rate of change of function y = 4x + 2
Thus, the statement that correctly compares the function shown on the 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.'
Hence, The correct answer is option (A)
Learn more about the rate of change of function here:
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