Question

What are the domain and range of the function mc012-1.jpg?
domain: mc012-2.jpg
range: mc012-3.jpg
domain: mc012-4.jpg
range: (0,mc012-5.jpg)
domain: mc012-6.jpg
range: mc012-7.jpg
domain: mc012-8.jpg
range: mc012-9.jpg

Answer 1

I can’t see the images you referenced. Please either upload mc012-1.jpg (the function or graph) or type the function or describe the graph. Once I can see it I’ll pick the correct domain and range from your option list.

Meanwhile, here’s how to find domain and range so you can check quickly:

Domain (allowed x-values)
- For an algebraic expression: exclude x that make a denominator 0 and exclude x that make an even root of a negative number or make the argument of a log ≤ 0.
- For a graph: project the graph onto the x-axis and report the x-values covered, using open/closed endpoints depending on holes/solid dots. Use union for separated intervals.

Range (possible y-values)
- For an algebraic expression: solve y = f(x) for x (or consider inverse) or analyze behavior (limits, asymptotes, vertex of quadratics).
- For a graph: project the graph onto the y-axis; note horizontal asymptotes, minima/maxima, and open/closed endpoints.

Common examples:
- f(x)=√(x−2) → domain [2, ∞), range [0, ∞).
- f(x)=1/(x−3) → domain (−∞,3) ∪ (3,∞), range (−∞,0) ∪ (0,∞).
- f(x) = (x−1)^2 + 2 → domain (−∞,∞), range [2,∞).

Send the image or the function and I’ll give the exact domain and range and pick the matching option.