Question

Describe the transformation.y = - [xl-5reflect over x-axis, vertical compress by factor of 3, and shift down 5reflect over x-axis, vertical compress by factor of 3, and shift up 5reflect over x-axis, vertical stretch by factor of 2, and shift down5reflect over x-axis, vertical stretch by factor of 2, and shift up 5

Answer 1

we have the equation

`y=-(1)/(3)\mleft|x\mright|-5`

the parent function is

`y=\mleft|x\mright|`

so

the transformations of the parent function to the given equation are

1) Reflection over x-axis

the rule is

(x,y) -------> (x,-y)

so

`\mleft|x\mright|---\longrightarrow\text{ -}\mleft|x\mright|`

2) vertical compress by factor of 3

`-|x|---\longrightarrow\text{ -}(1)/(3)|x|`

3) shift down 5

`\text{-}(1)/(3)|x|---\longrightarrow\text{ -}(1)/(3)|x|-5`

therefore

the answer is

reflect over x-axis, vertical compress by factor of 3, and shift down 5