Answer: g(x) = 3*Ix + 2I - 5
Step-by-step explanation:
First, let's define the transformations in a general way.
A vertical stretch of a scale factor A, is written as:
g(x) = A*f(x)
A vertical shift of A units is written as:
g(x) = f(x) + A
if A is positive, the shift is up, if A is negative, the shift is down.
A horizontal shift of A units is written as:
g(x) = f(x - A)
If A is positive, the shift is to the right.
If A is negative, the shift is to the left.
Then we start with the absoulte value parent function f(x) = IxI
"The graph of the absolute value parent function is vertically stretched by a factor of three"
We start with:
g(x) = 3*f(x)
"then shifted two units left"
g(x) = 3*f(x - (-2))
"and five units down."
g(x) = 3*f(x + 2) - 5.
and knowing that f(x) = IxI, we have:
g(x) = 3*Ix + 2I - 5
