What is the domain of this function? (Enter your answer using interval notation. What is the range of this function? (Enter your answer using interval notation.))

Question

f(x)= { 2x + 2 if 0< x ≤ 2

42 - x^2 if 2 < x ≤ 6

The two functions are part of a piece-wise function

Answer 1

(0,6] = the domain of f(x)

0<x<6

0<x<2 or 2<x<6

(0,2] U (2,6] = (0,6]

any other x value is undefined

range = (2,38]

range = (2,6] U (6,38] = (2,38]

2(0)+2 = 2

2(2)+2 = 6

42-2^2 = 38

42-6^2 = 6