Question

Which equation represents the transformation of f(x)=|x| when effected by a vertical stretch of 3, a horizontal shift to the right 4 units, and a vertical shift up 2 units?g(x)=13|x−4|+2g(x)=13|x+4|−2g(x)=3|x−4|+2g(x)=3|x+4|+2

Answer 1

Given:

$f(x)=\lvert x\rvert$

For vertical stretch of 3 is:

$\begin{gathered} f(x)=\lvert x\rvert \\ 3\text{ unit vertical stretch is:} \\ f(x)=3\lvert x\rvert \end{gathered}$

For shift the right 4 unit is:

use minues the unit for shift right for shift left add the units. so:

$\begin{gathered} f(x)=3\lvert x\rvert \\ 4\text{ units horizontal right shift:} \\ f(x)=3\lvert x-4\rvert \end{gathered}$

For vertical up:

Add the units for up shift the graph then:

$g(x)=3\lvert x-4\rvert+2$