Question

Below is the graph of f(x) = 3 10910*. How would you describe the graph ofg(x) = 910910 ?A312-23-3A. g(x) compresses f(x) by a factor of 3.B. g(x) stretches f(x) vertically by a factor of 3.C. g(x) shifts f(x) up 3 units.D. g(x) shifts f(x) to the right 3 units.

Answer 1

g(x) stretches f(x) vertically by a factor of 3 (option B)

Step-by-step explanation:

`f(x)=3log_(10)\text{ x}`
`\begin{gathered} g(x)\text{ = 9}log_(10)\text{ x} \\ g(x)=3(3log_(10)\text{ x)} \end{gathered}`

The transformation from f(x) to g(x):

`\begin{gathered} \text{the function of f(x) was multiplied by a scale factor of 3 to get g(x)} \\ g(x)\text{ = 3f(x)} \end{gathered}`

This shows a vertical stretch of 3

Hence, g(x) stretches f(x) vertically by a factor of 3 (option B)