Begin by graphing the standard absolute value function f(x) = | x |. then use transformations of this graph to describe the graph the given function.

h(x) = 2 | x | + 2

The  parent function f(x) is given by:

The transformed function h(x) is given by:

We know that the graph of the function g(x) is a vertical stretch  of the graph of the parent function plus a translation of the function 2 units up.

( Since if f(x) → a f(x)

Then the function is a vertical stretch if |a|>1 and a vertical compression if 0<|a|<1  

Also, a function f(x) → f(x)+k is shifted k units up or down depending on whether k>0 or k<0 respectively )

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

55% are girls and 45% are boys : ) hope this

step-by-step explanation: