The domain of the function f(x)=3x-6/x+4.5 (-3,-1, 2, 4,5). What is the function's range?
• The range for the given domain of the function f(x) = 3x-6/x+4.5 is

D ) Range={9.5, 13.5, 4.5, 6, 6.3}

Step-by-step explanation:

The function is f(x)=3x-6/x+4.5

the range is the set of all the values produced when we calculate f of all values in the domain.

so Range={f(-3), f(-1), f(2), f(4), f(5)}

Taking it one by one

f(x) = (3x-6/x)+4.5

F(3) = (3(-3)-6/3)+4.5 = (-9-6/-3)+4.5= (-15/-3)+4.5 = 5+4.5 = 9.5

f(-1) = (3(-1)-6/-1)+4.5 = (-3-6/-1)+4.5= (-9/-1)+4.5 = 9 +4.5 = 13.5

f(2) = (3(2)-6/2)+4.5= (6-6/2)+4.5 = (0/2)+4.5 = 0 +4.5 = 4.5

f(4) = (3(4)-6/4)+4.5= (12-6/4)+4.5 = (6/4)+4.5 = 1.5+4.5 = 6

f(5) = (3(5)-6/5)+4.5= (15-6/5)+4.5 = (9/5)+4.5 = 1.8 +4.5 = 6.3

The range for the given domain of the function f(x) = 3x-6/x+4.5 for {-3,-1,2,4,5} is {9.5,13.5,4.5,6,6.3}

D ) Range={9.5, 13.5, 4.5, 6, 6.3}