Function notation is a compact way to name a rule and show how an input becomes an output. This cheat sheet helps students read expressions like , evaluate functions from formulas, tables, and graphs, and avoid confusing notation with multiplication. It is useful for algebra, graphing, and real-world modeling because functions describe relationships between changing quantities.
The most important idea is that means the output of function when the input is . To evaluate a function, substitute the given input everywhere the variable appears, then simplify carefully using order of operations. Students should also connect notation to tables, graphs, domain, range, and compositions such as .
Key Facts
- Function notation means the value of the function at input , not .
- To evaluate , replace every in the formula for with and simplify.
- If , then .
- The input values of a function make up the domain, and the output values make up the range.
- A relation is a function if each input has exactly one output .
- On a graph, is the -value of the point on the graph where .
- For a table, is found by locating the row where the input is and reading the matching output.
- For a composite function, means evaluate first, then use that result as the input for .
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