Question

Which statement correctly compares the two functions given below

Answer 1

The functions:

`\begin{gathered} f(x)=(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(1)/(3)=(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.