The function [tex]g(x)=\dfrac{1}{3}f(x)[/tex] is best represented by the graph of g. Option B is correct.
Given information:
From the given graph of functions f and g, it can be observed that the inclination of f is more than that of function g.
Inclination signifies the angle it makes with the x-axis and slope is the tan of inclination. Greater the value of the slope, greater will be the inclination.
From the graph, the slope of function f is more than the slope of function g. Functions f and g pass through the origin and they both are straight lines.
So, dividing the function f(x) by a constant will reduce the slope of the function g(x). So, the correct function should be [tex]g(x)=\dfrac{1}{3}f(x)[/tex].
Function g(x) = f(x) − 4 represents that the slope of f and g is same. So, it is incorrect.
Function g(x) = f(x) − 2 represents that the slope of f and g is same. So, it is incorrect.
Function g(x) = 3f(x) represents that the slope of g is three times that of f. So, it is incorrect.
Therefore, the function [tex]g(x)=\dfrac{1}{3}f(x)[/tex] is best represented by the graph of g. Option B is correct.
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