Finding Domain and Range?

Question

Problem:

g(x)=abs(2x-8)+1


abs means the absolute value.

Answer 1

the domain for absolute function is always all real numbers or (-∞,∞)

the range is from y-intercept to infinity or [1, ∞)

note basicly if you wanna find range you have to look at graph , you can see this graph will start at minimum point is 1 and keep going up that is infinity so range is [1,∞)

if your graph upside down i meant if you have y = -|2x-8| +1
then graph will upsides down and starting at 1 and keep going down then
range will be (-∞, 1] because the small number will go first -∞ is small than 1 so they have to go first and 1 go later

Answer 2

Find the domain and range of

g(x) = | 2x - 8 | + 1

The domain is all real numbers, (-∞, ∞).

The range is [1, ∞).

An absolute value is never negative. The lowest it can be is zero. This occurs when x = 4.

At that point you have 0 + 1 = 1. This is the minimum value.