Question

What is the equation of the function shown in the graph, given that the equation of the parent function is f(x) = (1/4)^x ?A) g(x) = (1/4)^x - 4B) g(x) = (1/4)^x - 3C) g(x) = (1/4)^x - 2D) g(x) = (1/4)^x - 1

Answer 1

$\begin{gathered} f(x)=(\frac{1}{4})^x \\ \end{gathered}$

Let's find the y-intercept:

$\begin{gathered} x=0 \\ f(0)=(\frac{1}{4})^0 \\ f(0)=1 \end{gathered}$

As we can see the parent function crosses the y-axis at (0,1), since the new graph crosses the y-axis at (0,-2), then:

$\begin{gathered} 1-b=-2 \\ b=3 \end{gathered}$

Therefore, we need to translate the function f(x) 3 units down in order to get g(x), so:

$g(x)=(\frac{1}{4})^x-3$