#1**+2 **

The given function transforms the parent function, y = abs (x), in the following ways

a. Reflects the function across the x axis [ due to the negative sign]

b. Vertically "compresses" the function by (1/2)

c. Shifts this end result up by 3 units

"Vertex" = ( 0,3)

Domain = ( -infinity, +infinity)

Range = ( -infinity ....1,2,3] set builder notation

Range = ( -infinity, 3 ] interval notation

Zeroes x = -6 , x = -6

Y intercept = occurs at the vertex ⇒ (0,3)

Intervals of increase = (- infinity, 0)

Intervals of decrease = (0, infinity )

The end behavior in both directions is toward -infinity

Here's the parent graph and the given graph : https://www.desmos.com/calculator/tb3pt4duib

CPhill
Sep 24, 2017