Write the equation of G(x)

2 answers
Question:

Write the equation of G(x)

Answers

Answer: [tex]G(x)=\frac{1}{2}(x-3)^3+2[/tex]Step-by-step explanation:The given function is [tex]F(x)=x^{3}[/tex]The transformations to this graph are  in the form;[tex]G(x)=a(x-b)^3+c[/tex]where [tex]a=\frac{1}{2}[/tex] is the vertical compression by a factor of [tex]\frac{1}{2}[/tex] b=3 is a shift to the right by 3 units.c=2 is an upward shift by 2 units.Therefore [tex]G(x)=\frac{1}{2}(x-3)^3+2[/tex]

Answer:The equation is [tex]G(x)=-\frac{1}{2}(x-3)^3 +2[/tex]Step-by-step explanation:If the graph of the function [tex]G(x)=cf(x+h) +b[/tex]  represents the transformations made to the graph of [tex]y= f(x)[/tex]  then, by definition:If  [tex]0 <|c| <1[/tex] then the graph is compressed vertically by a factor c.If  [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor cIf [tex]c <0[/tex]  then the graph is reflected on the x axis.If [tex]b> 0[/tex] the graph moves vertically upwards.If [tex]b <0[/tex] the graph moves vertically downIf [tex]h <0[/tex] the graph moves horizontally h units to the rightIf [tex]h >0[/tex] the graph moves horizontally h units to the leftIn this problem we have the function [tex]G(x)[/tex] and our parent function is [tex]f(x) = x^3[/tex]We know that G(x) is equal to f(x) but reflected on the x-axis ([tex]c <0[/tex]), compressed vertically by a multiple of 1/2 ([tex]0 <|c| <1[/tex] and [tex]c = -\frac{1}{2}[/tex]), displaced 2 units upwards ([tex]b = 2>0[/tex]) and moved to the right 3 units ([tex]h = -3<0[/tex])Then:[tex]G(x)=-\frac{1}{2}f(x-3) +2[/tex][tex]G(x)=-\frac{1}{2}(x-3)^3 +2[/tex]

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