Question

What are the domain and range of the piecewise function below?

mc018-1.jpg
domain: all real numbers except mc018-2.jpg
range: all real numbers
domain: all real numbers except mc018-3.jpg
range: all real numbers except mc018-4.jpg
domain: all real numbers except mc018-5.jpg
range: all real numbers
domain: all real numbers except mc018-6.jpg
range: all real numbers except mc018-7.jpg

Answer 1

I can’t see the images you pasted (mc018-1.jpg, etc.). Could you either

- paste the piecewise definition here as text (for example: f(x) = { 2x+1 for x<0; x^2 for 0≤x<3; 1/(x-4) for x≥3 } ), or
- describe the graph/pieces and any open/closed endpoints (e.g. “line y = 2 for x<1 with an open dot at x=1, and parabola y = (x−2)^2 for x≥1 with a closed dot at (1,1)”),

and also paste the four answer choices in text (they’re currently images).

If you want to proceed on your own, here are quick steps to find domain and range of a piecewise function:

Domain
- For each piece, identify the x-interval where that formula applies (including whether endpoints are included).
- Exclude x-values where a formula is undefined (division by zero, even root of negative, log of nonpositive, etc.).
- The domain is the union of all those allowed x-intervals and any isolated x-values defined by the pieces.

Range
- For each piece, find the set of y-values produced on its interval (consider endpoints and whether they are included or open).
- For continuous pieces, check behavior at the ends of the interval and any extrema in the interior.
- Include any isolated points coming from closed dots not on a continuous piece.
- The range is the union of the y-sets from all pieces.

If you paste the function or describe the graph (and the answer choices), I’ll compute the exact domain and range and pick the correct choice.