The graph of f(x) = x is simply a straight line that passes through the origin with a slope of 1. It increases one unit up for every unit it moves to the right.
The graph of g(x) = 6f(x) is also a straight line, but since g(x) = 6x (substituting f(x) with x), the slope of this line is 6. This means that g(x) increases six units up for every unit it moves to the right.
Therefore, the correct relationship between the graphs of f and g is:
The graph of g is steeper than the graph of f.
The other options are incorrect because multiplying the function by 6 affects the slope, not the position. There is no shifting up or down, and the graph of g(x) is steeper, not less steep, than that of f(x).
A student graphed f(x)=x and g(x)=6f(x) on the same coordinate grid. Which statement best describes how the graphs of f and g are related?
A student graphed f(x)=x and g(x)=6f(x) on the same coordinate grid. Which statement best describes how the graphs of f and g are related?
The graph of g is steeper than the graph of f.
The graph of f is shifted 6 units down to create the graph of g.
The graph of g is less steep than the graph of f.
The graph of f is shifted 6 units up to create the graph of g.
1 answer