The graph of f(x)=x is transformed to create the graph of g(x)=af(x). If a is a whole number greater than 1, what conclusion can be drawn?
The graph of f(x)=x is transformed to create the graph of g(x)=af(x). If a is a whole number greater than 1, what conclusion can be drawn?
The graph of g(x) is less steep than f(x).
The graph of g(x) is translated a units down.
The graph of g(x) is steeper than f(x).
The graph of g(x) is translated a units up.
Let's analyze the transformation described.
Given f(x) = x, this is the equation of a straight line with a slope of 1, meaning it increases by 1 unit in the y-direction for every 1 unit increase in the x-direction.
Now consider the graph of g(x) = af(x), where a is a whole number greater than 1. Since f(x) = x, this means g(x) = ax. What this does is multiply every y-value by a for the corresponding x-value in the graph of f(x).
Since a is greater than 1, the effect is to make the graph steeper. Specifically, for every 1 unit increase in the x-direction, g(x) now increases by a units in the y-direction, rather than just 1 unit as was the case with f(x). This means that at any given x-value (except for x=0), the point on g(x) will be a times higher than the corresponding point on f(x).
Therefore, the correct conclusion that can be drawn from the transformation g(x) = af(x) is:
The graph of g(x) is steeper than f(x).