Your friend attempted to describe the transformations applied to the graph of y=sinx to give the equation f(x)=1/2sin(-1/3(x+30))+1.

CMIIh 2021-02-11 Answered

Your friend attempted to describe the transformations applied to the graph of \(y=\sin x\) to give the equation \(f(x)=\frac{1}{2} \sin(-\frac{1}{3}(x+30))+1\).
They think the following transformations have been applied. Which transformations have been identified correctly, and which have not? Justify your answer.
a) f(x) has been reflected vertically.
b) f(x) has been stretched vertically by a factor of 2.
c) f(x) has been stretched horizontally by a factor of 3.
d) f(x) has a phase shift left 30 degrees.
e) f(x) has been translated up 1 unit.

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Expert Answer

Bentley Leach
Answered 2021-02-12 Author has 16948 answers

Given
Your friend attempted to describe the transformations applied to graph of
\(\Rightarrow f(x)=\frac{1}{2}\sin(-\frac{1}{3}(x+30))+1\)
a)f(x) has been reflected vertically
\(\Rightarrow\) No, the f(x) has been reflected horizontally.
b)f(x) has been stretched vertically by a factor of 2.
\(\Rightarrow\) No, the f(x) has been compressed by a factor of \(\frac{1}{2}\).
c)f(x) has been stretched horizontally by a factor of 3.
\(\Rightarrow\) No, the f(x) has been stretched horizontally by a factor of \(\frac{1}{3}\)
d)f(x) has a phase shift left 30 degrees
\(\Rightarrow\) Yes, f(x) has a shift left 30 degrees
e)f(x) has been translated up 1 unit
\(\Rightarrow\) Yes, f(x) has been translated up 1 unit

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