Functions: Domain/Range, Key Features, and Inverses
Lessons in this chapter
About Functions: Domain/Range, Key Features, and Inverses
Functions: Domain/Range, Key Features, and Inverses builds the complete function vocabulary that every later function family in this course assumes.
Relations and Functions reviews the one-output-per-input rule from 8th grade, before Domain and Range of a Function names the full set of valid inputs (domain) and resulting outputs (range) for a given function.
Function Notation introduces f(x) as a way to name a function and describe evaluating it at a specific input, while Key Features of the Graph of a Function has kids read intercepts, intervals of increase and decrease, and maximum or minimum points directly from a graph.
Inverse of a Function closes the chapter by reversing a function's input-output pairs entirely, finding the rule that undoes the original function, and verifying two functions are true inverses by checking that composing them returns the original input.
The five lessons in this chapter each open as an Algebra 1 worksheet in the page, including Domain and Range of a Function, Function Notation and Inverse of a Function. Every question is scored as it is answered, so reading f(3) as multiplication rather than as the output at x = 3 gets caught on the spot. The practice is free to try, with no login needed for your first 3.
Frequently asked questions
Relations and Functions draws the line between a relation and a function, Domain and Range of a Function names the set of inputs and the set of outputs, and Function Notation replaces y with f(x) so a particular output can be asked for directly. Key Features of the Graph of a Function reads intercepts, increasing and decreasing intervals and maximum and minimum points off a graph, and Inverse of a Function undoes the rule by swapping inputs and outputs. The chapter sits in the high school Functions conceptual category (F).
The domain is the complete set of valid input values a function can accept; the range is the complete set of output values it can actually produce.
f(x) names a function f and represents its output when evaluated at input x: f(3) means "the output of function f when the input is 3," not f multiplied by x.
Key features include intercepts (where the graph crosses the axes), intervals where the function increases or decreases, and any maximum or minimum points: all readable directly from a graph without needing the equation.
The inverse of a function reverses every input-output pair. If f(2) = 7, then the inverse function has an input of 7 producing an output of 2: essentially undoing what the original function does.
Swap x and y in the function's equation, then solve for y. This reflects the fact that an inverse function swaps every input with its corresponding output.