Question

Tammy is playing pool and wants to win the game by hitting the eight ball into the corner pocket. If the eight ball will hit the wallher goal is the corner pocket (8, 4) effect does the transformation shown on the graph have on the function

Answer 1

Transformation involves changing the size and location of a function.

$\mathbf{y = 2|x - 6|}$ is produced by a vertical stretch, and a horizontal shift left.

An absolute function is represented as:

$\mathbf{y = a|x - h| + k}$

The parameters are represented as:

$\mathbf{(h,k) = (6,0)}$ --- vertex

$\mathbf{(x,y) = (8,4)}$ --- point

Substitute $\mathbf{(h,k) = (6,0)}$ and $\mathbf{(x,y) = (8,4)}$ in $\mathbf{y = a|x - h| + k}$

$\mathbf{4 = a|8 - 6| + 0}$

$\mathbf{4 = a|8 - 6|}$

$\mathbf{4 = a|2|}$

Remove absolute brackets

$\mathbf{4 = a \times 2}$

Divide both sides by 2

$\mathbf{a= 2}$

Substitute $\mathbf{a= 2}$ and $\mathbf{(h,k) = (6,0)}$ in $\mathbf{y = a|x - h| + k}$

$\mathbf{y = 2|x - 6| + 0}$

$\mathbf{y = 2|x - 6|}$

The parent function of an absolute function is:

$\mathbf{y = |x|}$

A right translation is represented as:

$\mathbf{y = |x - h|}$

And a vertical stretch is represented as:

$\mathbf{y = a|x - h|}$

Hence,

$\mathbf{y = 2|x - 6|}$ is produced by option (d)

Read more about transformations at:

brainly.com/question/13801312