Question

What transformations are needed to change the parent cosine function to y=3cos(10(x-pi))?

Answer 1

Answer:

The graph of $y=cos(x)$ is:

*Stretched vertically by a factor of 3

*Compressed horizontally by a factor  $\frac{1}{10}$ .

*Moves horizontally $\pi$ units to the rigth

The transformation is:

$y=3f(10(x-\pi))$

Step-by-step explanation:

If  the function $y=cf(h(x+b))$  represents the transformations made to the graph of $y= f(x)$  then, by definition:

If  $0$ then the graph is compressed vertically by a factor c.

If  $|c| > 1$ then the graph is stretched vertically by a factor c

If $c$  then the graph is reflected on the x axis.

If $b> 0$ The graph moves horizontally b units to the left

If $b$ The graph moves horizontally b units to the rigth

If $0$ the graph is stretched horizontally  by a factor $\frac{1}{h}$

If $h> 1$ the graph is compressed horizontally by a factor $\frac{1}{h}$

In this problem we have the function $y=3cos(10(x-pi))$ and our parent function is $y = cos(x)$

The transformation is:

$y=3f(10(x-\pi))$

Then $c =3>1$  and $b =-\pi < 0$ and $h=10 > 1$

Therefore the graph of $y=cos(x)$ is:

Stretched vertically by a factor of 3.

Also as $h=10$ the graph is compressed horizontally by a factor  $\frac{1}{10}$ .

Also, as $b =-\pi < 0$ The graph moves horizontally $\pi$ units to the rigth