1.1 Domain and Range
Every function is like a machine. You feed a number in (that's the input), the machine processes it, and a number comes out (the output). The domain is the set of all input values (x-values) that the machine will accept without breaking. The range is the set of all possible outputs (y-values) that can come out.
Domain = "What x-values am I allowed to use?" — scan the graph left ↔ right Range = "What y-values can come out?" — scan the graph up ↕ down Two things restrict the domain: square roots (you can't take the square root of a negative number) and division (you can't divide by zero).
f(x) = x Domain: all reals, Range: all reals f(x) = x² Domain: all reals, Range: [0, ∞) ← y is never negative f(x) = √x Domain: [0, ∞), Range: [0, ∞) ← x must be ≥ 0 f(x) = |x| Domain: all reals, Range: [0, ∞) ← output is always ≥ 0 f(x) = 1/x Domain: x ≠ 0, Range: y ≠ 0 ← never equals 0
📝 Practice Workbook Problems
Ready to take the Chapter 1 Quiz?
6 timed problems · Detailed explanations for every answer.