Answer:
Option C.The range changes from {y | y > 0} to {y | y > 2}.
Step-by-step explanation:
The complete question is
The graph of f(x) = |x| is translated 6 units to the right and 2 units up to form a new function. Which statement about the range of both functions is true?
A.The range is the same for both functions: {y | y is a real number}.\
B.The range is the same for both functions: {y | y > 0}.
C.The range changes from {y | y > 0} to {y | y > 2}.
D.The range changes from {y | y > 0} to {y | y > 6}.
we have
[tex]f\left(x\right)=\left|x\right|[/tex]
The vertex of this function is the point (0,0)
The range of f(x) is the interval [0,∞)
If f(x) is is translated 6 units to the right and 2 units up to form a new function g(x)
then
The rule of the translation of f(x) to g(x) is
(x,y) ----> (x+6,y+2)
The new vertex is
(0,0) ---> (0+6,0+2)
(0,0) ---> (6,2)
so
The new function equation is
[tex]g\left(x\right)=\left|x-6\right|+2[/tex]
The range of g(x) is the interval [2,∞)
therefore
The statement that is true is
The range changes from {y | y > 0} to {y | y > 2}.
