Answer to Question #194198 in Calculus for Peter

Question

Write a formula for the function g(x) that results when the graph of f(x)=x²     is horizontally stretched by a factor of 3, then shifted to the left 4 units, and then shifted down 3 units . Sketch the graph of f(x)  fas well as the graph of the new transformed function g(x)   

g(x)=? 

Answer 1

$f(x)=x^2.\newline \text{horizontally stretched by a factor of 3.}\newline a(x)=f(\frac{x}{3})=\frac{x^2}{9}\newline\text{ shifted to the left 4 units,}\newline b(x)=a(x+4)=f(\frac{x+4}{3})=\frac{(x+4)^2}{9}\newline\text{ shifted down 3 units,}\newline g(x)=b(x)-3=a(x+4)-3=f(\frac{x+4}{3})-3=\frac{(x+4)^2}{9}-3\newline\text{ Then, the required }g(x)=\frac{(x+4)^2}{9}-3.\newline$