Determine the domain and range of a function from its equation or graph, and evaluate functions fluently using interval notation.
In Algebra I you met f(x) notation and learned to evaluate a function at a value. This year leans on that skill constantly, so we start by sharpening it: every function has a domain (the complete set of x-values you are allowed to feed in) and a range (the complete set of outputs that come back out). Get sloppy about domain now, and rational expressions, radicals, and logarithms later this year will punish you for it.
Finding domain is mostly hunting for trouble: a fraction breaks when its denominator is 0, and a square root breaks when the inside is negative (we work with real numbers only, so no real square root of a negative number exists yet -- that changes in a few months). Range is usually easier to see from a graph or by reasoning about what values an expression can actually produce. We will also write domain and range in interval notation: a bracket [ or ] means the endpoint IS included; a parenthesis ( or ) means it is not (or that the interval runs off to infinity, which is never actually reached).
Mastery looks like: They find the domain of a rational or square-root function without prompting, write it correctly in interval notation, and evaluate the function at a given input.
Common stumbles: Forgetting to exclude the denominator-zero value from the domain; writing the range instead of the domain (or vice versa) when asked.