Question

If mc021-1.jpg and mc021-2.jpg, what is the range of mc021-3.jpg?
mc021-4.jpg
mc021-5.jpg
mc021-6.jpg
mc021-7.jpg

Answer 1

I can't see the image files you referenced. Could you either upload the images or paste the function/graph description here?

Meanwhile, here is how to find the range depending on what you have:

- If you have a graph:
- Find the lowest and highest y-values that the graph attains.
- Check whether those extreme values are included (solid dot or closed interval) or excluded (open dot).
- Look for horizontal asymptotes — values the graph approaches but does not reach are excluded from the range.
- If the graph continues up/down without bound, the range is unbounded in that direction (use ∞ or −∞).

- If you have an equation:
- For y = f(x) algebraically, solve for x in terms of y (i.e. x = g(y)) and determine which y give real x.
- For common functions:
- Quadratic with vertex at (h,k) opening up: range [k, ∞)
- Quadratic opening down: (−∞, k]
- Square root: [value at left endpoint, ∞)
- Rational: watch for horizontal asymptotes and excluded values
- Absolute value with vertex at (h,k): [k, ∞)

If you upload (or describe) the specific images mc021-3.jpg (and mc021-1/2 if they’re needed), I’ll compute the exact range.