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# f(x)= square root x + 2 - 3

how do you find the domain and range of this equation? I have already graphed the equation, but I don't know how to find the domain and range of this equation.... please help me. I need the answer.

### 2 Answers by Expert Tutors

Kathye P. | Math Geek, passionate about teachingMath Geek, passionate about teaching
5.0 5.0 (150 lesson ratings) (150)
1

Hi, The.

The domain of a function is the set of all possible values for x. The range is all possible values for y.

You should be able to see these pretty easily from the graph. If I understand your function correctly:

f(x) = square root(x+2) - 3

then x cannot be less than -2. Your domain is x > -2. In interval notation [-2,∞)

The lowest value for y is -3 so the range is y > -3. In interval notation [-3,∞)

Hope this helps!

Kathye P.

Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
1

f(x) = √(x+2) - 3 <== Is this what you meant?

Domain: √(x+2) ≥ 0 ==> x ≥-2. So the domain is [-2, ∞)

Range: [-3, ∞), since √(x+2) ≥ 0, f(x) ≥ -3.