Write a rule for g that represents a translation 3 units right and 1 unit up, followed by a horizontal stretch by a factor of 8 of the graph of f(x)=lnx.

Answer 1

Translation 3 units right means you will group "3" with the "right-left" variable which is "x". But, "x" is the opposite of what it appears so to move right you must subtract 3 from "x" so ln(x) becomes ln(x - 3).

To move the function up 1 unit, simply add 1 to the function so ln(x -3) becomes ln(x - 3) + 1.

To stretch horizontally by a factor of 8 means you will multiply the "horizontal variable" (aka "x") by a factor but since "x" is the opposite of what it appears, you must actually divide by 8 (or multiply by 1/8). So the ln(x - 3) + 1 becomes ln[1/8(x - 3)] + 1.

So g(x) = ln[1/8(x - 3)] + 1.