# Key Concepts & Glossary

## Key Equations

Constant function | [latex]f\left(x\right)=c[/latex], where [latex]c[/latex] is a constant |

Identity function | [latex]f\left(x\right)=x[/latex] |

Absolute value function | [latex]f\left(x\right)=|x|[/latex] |

Quadratic function | [latex]f\left(x\right)={x}^{2}[/latex] |

Cubic function | [latex]f\left(x\right)={x}^{3}[/latex] |

Reciprocal function | [latex]f\left(x\right)=\frac{1}{x}[/latex] |

Reciprocal squared function | [latex]f\left(x\right)=\frac{1}{{x}^{2}}[/latex] |

Square root function | [latex]f\left(x\right)=\sqrt{x}[/latex] |

Cube root function | [latex]f\left(x\right)=\sqrt[3]{x}[/latex] |

## Key Concepts

- A relation is a set of ordered pairs. A function is a specific type of relation in which each domain value, or input, leads to exactly one range value, or output.
- Function notation is a shorthand method for relating the input to the output in the form [latex]y=f\left(x\right)[/latex].
- In tabular form, a function can be represented by rows or columns that relate to input and output values.
- To evaluate a function, we determine an output value for a corresponding input value. Algebraic forms of a function can be evaluated by replacing the input variable with a given value.
- To solve for a specific function value, we determine the input values that yield the specific output value.
- An algebraic form of a function can be written from an equation.
- Input and output values of a function can be identified from a table.
- Relating input values to output values on a graph is another way to evaluate a function.
- function is one-to-one if each output value corresponds to only one input value.
- A graph represents a function if any vertical line drawn on the graph intersects the graph at no more than one point.
- The graph of a one-to-one function passes the horizontal line test.

## Glossary

**dependent variable**- an output variable

**domain**- the set of all possible input values for a relation

**function**- a relation in which each input value yields a unique output value

**horizontal line test**- a method of testing whether a function is one-to-one by determining whether any horizontal line intersects the graph more than once

**independent variable**- an input variable

**input**- each object or value in a domain that relates to another object or value by a relationship known as a function

**one-to-one function**- a function for which each value of the output is associated with a unique input value

**output**- each object or value in the range that is produced when an input value is entered into a function

**range**- the set of output values that result from the input values in a relation

**relation**- a set of ordered pairs

**vertical line test**- a method of testing whether a graph represents a function by determining whether a vertical line intersects the graph no more than once

## Licenses & Attributions

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- Precalculus.
**Provided by:**OpenStax**Authored by:**Jay Abramson, et al..**Located at:**https://openstax.org/books/precalculus/pages/1-introduction-to-functions.**License:**CC BY: Attribution.**License terms:**Download For Free at : http://cnx.org/contents/[email protected]..