Question

What is the equation of the function shown in the graph, given that the equation of the parent function is f(x) = (1/3)^x ?A) g(x) = (1/3)^x - 2B) g(x) = (1/3)^x - 1C) g(x) = (1/3)^x + 1D) g(x) = (1/3)^x + 2

Answer 1

A)

`g(x)=\mleft((1)/(3)\mright)^x-2`

Explanation:

Given the parent function:

`f\mleft(x\mright)=\mleft((1)/(3)\mright)^x`

We evaluate this to zero to get the y-intercept:

`\begin{gathered} f(0)=\mleft((1)/(3)\mright)^0=1 \\ \text{ The y-intercept is y = 1} \end{gathered}`

While on the graph, the y-intercept is at y = -1

Therefore, it is 2 units below the y-intercept of the parent function, which means the function is translated 2 units down. This is reflected in the equation as a subtraction of 2 units from the parent function.

Therefore, the equation would be:

`g(x)=\mleft((1)/(3)\mright)^x-2`