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

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.

STEP 1:

shift the graph 8 units to the left

STEP 2

reflect the graph in the y-axis

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: