Question

a. List all transformations on the equation y = -2x +31 + 2 by graphing the parent function and using transformations. ( points) b. Identify the domain and range of the graph. 2 points)

Answer 1

we know that

the parent function of this problem is

$y=\mleft|x\mright|$

so the transformations are

First

A dilation of the y component with a scale factor of -2

the rule is

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

a=-2

$y=\mleft|x\mright|\text{ ---}\longrightarrow\text{ y=-2}\mleft|x\mright|$

Second

A translation of 3 units at left and 2 units up

the rule is

(x,y) ------> (x-3,y+2)

therefore

$\text{y=-2}|x|\text{ ----}\longrightarrow\text{ y=-2}\mleft|x+3\mright|+2$

using a graphing tool

see the attached image

please wait a minute

the domain is all real numbers

the range is the interval (-infinite, 2}