Question #194198

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)=? 



1
Expert's answer
2021-05-18T08:12:07-0400

f(x)=x2.horizontally stretched by a factor of 3.a(x)=f(x3)=x29 shifted to the left 4 units,b(x)=a(x+4)=f(x+43)=(x+4)29 shifted down 3 units,g(x)=b(x)3=a(x+4)3=f(x+43)3=(x+4)293 Then, the required g(x)=(x+4)293.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


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