# Points, Vectors, and Functions

### Terms

### Function

A relation in which each input in the domain has one and only one output.### Increasing Function

A function in which the value of the output (the*y*value) increases as the input value (the

*x*value) increases.

### Decreasing Function

A function in which the value of the output (the*y*value) increases as the input value (the

*x*value) increases

### Even Function

A function*f*(

*x*) in which all values of

*x*in the domain

*f*(

*x*) =

*f*(-

*x*); equivalently, the graph of

*f*(

*x*) is symmetric with respect to the

*y*-axis.

### Odd Function

A function*f*(

*x*) in which all values of

*x*in the domain

*f*(

*x*) = -

*f*(-

*x*); equivalently, the graph of

*f*(

*x*) is symmetric with respect to the origin.

### Bounded Function

A function*f*(

*x*) is bounded if

*f*(

*x*) is less than or equal to a constant |

*f*(

*x*)| <=

*M*for all values of

*x*in the domain.

### Unbounded Function

A function*f*(

*x*) is unbounded if a constant

*M*such that |

*f*(

*x*)| <=

*M*does not exist for all values of

*x*.

### Vector

A mathematical structure that has both magnitude and direction, represented by an ordered pair of components.### Magnitude Of A Vector

The length of a vector, denoted by || ||.### Direction Of A Vector

The counter-clockwise angle from the positive*x*-axis to the vector.

### Unit Vector

Vector with magnitude 1.### Parametric Equation

A set of equations describing relations between variables using parameters.### Polar Coordinate

A point represented in terms of its distance from the origin and angle from the*x*-axis.

### Cartesian/Rectangular Coordinate

A point represented in terms of its distance from the*x*-axis and

*y*-axis.

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