Graph functions

Horizontal Line test

If a graph passes the horizontal line test it has an inverse that is a function. A horizontal line can only pass through one point on the graph. The image fails so inverse is NOT a function.

Relative maximum

Over a specific domain the maximum value the graph reaches, the max is the y-coordinate.

Relative minimum

Over a specific domain the minimum value of the graph reaches, the minimum is the y-coordinate. Has a min at (3,-5) min value of -5

Domain

Possible x-values of the function. In graph above (-∞,∞)

Range

Possible y-values of the function In graph [5,∞)

piecewise

a function defined differently over various domains.

One-to-One

A function that passes both the horizontal and vertical line test. Each value of x goes to a unique value for y.

Inverse

Switch the x, and y values of the points. Is the graph reflected along y = x. The red and blue are inverses, the black is y=x

decreasing

The x-values over which a function is going down from left to right. Decreasing: (-∞,3)

Increasing

The x-values over which a function is going up from left to right. (3,∞) Increasing in graph.

constant

The x-values over which a function stays the same. Constant[3,∞)

Vertical Line test

Used to test if a graph is a function. Vertical line can NOT go through the graph in more than one location to be a function. The image passes so is a function.

x-intercept(s)

Where the graph crosses the x-axis In graph: 1 and 5

y-intercepts

Where the graph crosses the y-axis. In graph 3.5