Given the functions:
• f(x) = sin(-x)
,
• f(x) = sin(2x)
,
• f(x) = sin(1/2x)
Given that each function is a transformation of the parent sine function, let's select the graph which represents each transformed function.
We have the parent sine function:
f(x) = sin(x).
• For function A.
f(x) = sin(-x)
The graph of this transformed function will be:
• For function B.
f(x) = sin(2x)
The period of this function will be:
[tex]T=\frac{2\pi}{B}=\frac{2\pi}{2}=\pi[/tex]
Therefore, the graph which represents this function is:
• Function C.
f(x) = sin(1/2x)
The period of this function will be:
[tex]T=\frac{2\pi}{B}=\frac{2\pi}{\frac{1}{2}}=4\pi[/tex]
Therefore, the graph of this function will be:
ANSWER:
