Answer: Third option.
Step-by-step explanation:
We know that the sine function is:
[tex]f(x)=Asin(bx)[/tex]
Where "A" is the amplitude of the function( This is half the vertical distance between minimum value and maximum value of the function) and [tex]\frac{2\pi }{b}[/tex] is the period.
Observe in the graph that the amplitude is:
[tex]A=1[/tex]
And the period is 1, then "b" is:
[tex]1=\frac{2\pi }{b}\\\\b=\frac{2\pi }{1}\\\\b=2\pi[/tex]
Then the function shown in the graph is:
[tex]f(x)=sin(2\pi x)[/tex]
By definition in the transformation of the function:
When [tex]kf(x)[/tex] and [tex]k>1[/tex] then the function is stretched vertically by a factor of "k".
In this case we know that the function shown in the graph is vertically stretched by a factor of 2 to produce a new graph. Then:
[tex]k=2[/tex]
Therefore,the function that represents the new graph is:
[tex]f(x)=2sin(2\pi x)[/tex]
