Question

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.

Performing transformations

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.

2021-02-12

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