Question

For the two functions given as $f\left(x\right)=\ln (x-8)+7,g\left(x\right)=\ln x$,
which of the following denotes the transformations of the function $g\left(x\right)$ to obtain the function $f\left(x\right)$

• A. Translate $8$ units to the right and $7$ units down
• B. Translate $8$ units to the left and $7$ units up
• C. Translate $7$ units to the left and $8$ units down
• D. Translate $8$ units to the right and $7$ units up

Answer 1

The correct option is D Translate $8$ units to the right and $7$ units up

$g\left(x\right)=\ln x$
Let $h\left(x\right)=\ln (x-8)$
To create the graph of $h\left(x\right)$, graph of $g\left(x\right)=\ln x$ is shifted $8$ units to right.
Now for $f\left(x\right)=\ln (x-8)+7=h\left(x\right)+7$, graph of $h\left(x\right)=\ln (x-8)$ is shifted $7$ units up.