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.

Step-by-step 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 $\frac{2\pi }{b}$ is the period.

Observe in the graph that the amplitude is:

$A=1$

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

$1=\frac{2\pi }{b}\\\\b=\frac{2\pi }{1}\\\\b=2\pi$

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:

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