SOLUTION: if g(x) is a transformation of f(x), find the vertex of the g(x) and describe the transformation. f(x)=|x| g(x)=|x+3|-5

Algebra ->  Rational-functions -> SOLUTION: if g(x) is a transformation of f(x), find the vertex of the g(x) and describe the transformation. f(x)=|x| g(x)=|x+3|-5      Log On


   

Question 922529: if g(x) is a transformation of f(x), find the vertex of the g(x) and describe the transformation.
f(x)=|x|
g(x)=|x+3|-5
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
This is always true:
To shift a function left, add inside the function's argument: f%28x+%2B+b%29 gives f%28x%29 shifted b units to the left.
Shifting to the right works the same way; f%28x-b%29 is f%28x%29 shifted b units to the right.
if you have f%28x%29+%2B+a, means that f%28x%29 is shifted upward+a units
if you have f%28x%29-a, means that f%28x%29 shifted downward+a+ units
you are given:
f%28x%29=abs%28x%29
g%28x%29=abs%28x%2B3%29-5 => b=3=>f%28x%29 shifted 3 units to the left
and a=-5=>means that f%28x%29 shifted downward+-5+ units

+graph%28+600%2C+600%2C+-6%2C+5%2C+-10%2C+10%2C+abs%28x%29%2C+abs%28x%2B3%29-5%29+