Question

How to translate f(x)=ln(8-x) into g(x)=lnx

Answer 1

Step-by-step explanation:

f (x) + n → shifts the function n units upward.

f (x) – n → shifts the function n units downward.

f (x + n) → shifts the function n units to the left.

f (x – n) → shifts the function n units to the right.

–f (x) → reflects the function in the x-axis.

f (–x) → reflects the function in the y-axis.

$f(x)=\ln(8-x)=\ln\bigg(-(x-8)\bigg)\\\\h(x)=f(x+8)=\ln\bigg(-(x-8+8)\bigg)=\ln(-x)\\\\g(x)=h(-x)=\ln\bigg(-(-x)\bigg)=\ln(x)$

STEP 1:

shift the graph 8 units to the left

STEP 2

reflect the graph in the y-axis