Question

Let f(x)= -3x. The graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 and a translation of 4 units right. What is an equation for g(x)?

Answer 1

Translations to the left and right take the form f(x-s), where s is the value of the shift. Note that shifts in the positive (right) direction appear negative, and shifts in the negative (left) direction appear positive. It's common to mistake these, so memorize the rule! In this case, the shift becomes f(x-4) = -3(x-4). A vertical stretch takes the form of k*f(x), where k is the value of the stretch. This stretch would appear as 4*f(x) = 4(-3x). Combining these transformations would yeild 4*f(x-4) = 4[-3(x-4)]. Simplify for the final result.