Question

The function shown in the graph is vertically stretched by a factor of 2 to produce a new graph.

Which function represents the new graph?

Answer 1

Answer: Third option.

Explanation:

We know that the sine function is:

`f(x)=Asin(bx)`

Where "A" is the amplitude of the function( This is half the vertical distance between minimum value and maximum value of the function) and
`(2\pi )/(b)` is the period.

Observe in the graph that the amplitude is:

`A=1`

And the period is 1, then "b" is:

`1=(2\pi )/(b)\\\\b=(2\pi )/(1)\\\\b=2\pi`

Then the function shown in the graph is:

`f(x)=sin(2\pi x)`

By definition in the transformation of the function:

When
`kf(x)` and
`k>1` 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:

`k=2`

Therefore,the function that represents the new graph is:

`f(x)=2sin(2\pi x)`