which set of steps will translate $f(x)=6^{x}$ to $g(x)=6^{x - 5}-7$?\nshift $f(x)=6^{x}$ five units to the…

which set of steps will translate $f(x)=6^{x}$ to $g(x)=6^{x - 5}-7$?\nshift $f(x)=6^{x}$ five units to the left and seven units up.\nshift $f(x)=6^{x}$ five units to the right and seven units down.\nshift $f(x)=6^{x}$ seven units to the right and five units up.\nshift $f(x)=6^{x}$ seven units to the left and five units down.

which set of steps will translate $f(x)=6^{x}$ to $g(x)=6^{x - 5}-7$?\nshift $f(x)=6^{x}$ five units to the left and seven units up.\nshift $f(x)=6^{x}$ five units to the right and seven units down.\nshift $f(x)=6^{x}$ seven units to the right and five units up.\nshift $f(x)=6^{x}$ seven units to the left and five units down.

Answer

Explanation:

Step1: Recall horizontal shift rule

For a function $y = f(x - h)$, the graph of $y = f(x)$ is shifted $h$ units to the right. Given $f(x)=6^{x}$ and $g(x)=6^{x - 5}-7$, for the exponent part, comparing $6^{x}$ and $6^{x - 5}$, we have $h = 5$. So, $f(x)$ is shifted 5 units to the right.

Step2: Recall vertical shift rule

For a function $y=f(x)+k$, if $k>0$ the graph is shifted $k$ units up and if $k < 0$ the graph is shifted $|k|$ units down. In $g(x)=6^{x - 5}-7=6^{x - 5}+(- 7)$, since $k=-7$, $f(x)$ is shifted 7 units down.

Answer:

Shift $f(x)=6^{x}$ five units to the right and seven units down.