transformations

Question

given f(x) = 1/x

compress horizontally by a factor of 2

translate left 3 units

I need help trying to find the equation.

Answer 1

Compress hotizontally by a factor of 2

f(x) > f(2x) = 1/2x

translate left 3 units replace x by x+3

1/[2(x+3)]

Answer 2

Horizontal compression or stretch means multiplying the "x" by a factor. But you must treat the "x" as "Mr. Opposite" in that compression is multiplication by a number larger than 1 and stretch is multiplication be a number between 0 and 1 (this is opposite of the y-direction). Also translation is opposite - moving left means you group with the "x" an number larger than 0 (add to the "x") and translation right means grouping with the "x" a number less than 1 (subtracting from the "x").

So combining these, if g(x) is the transformed function, then: