Question

Which statement correctly compares the two functions given below

Answer 1

The functions:

$\begin{gathered} f(x)=\frac{1}{3}x+9 \\ g(x)=3x-11 \end{gathered}$

are linear functions. This means that they have the form:

$f(x)=mx+b$

where m is the slope (that represents the rate of change) of the function.

The function f has slope 1/3 and the function g has slope 3.

From this we notice that:

$9\cdot\frac{1}{3}=\frac{9}{3}=3$

Then we conclude that the function g grows at a rate nine times faster than f.

Therefore the correct statement is A.