Intro to Functions

A relation is any rule that connects two variables. A relation can connect both quantitative and qualitative variables

A variable is a placeholder for an unknown measurement. Since measuring is the act of sizing attributes, a variable represents an unknown aspect of an attribute.

Relations are important because they help us describe relationships between two values or concepts. They allow us to define, discuss, and use relationships between variables in problem-solving.

I can represent a relation verbally, in a table of values, as a set of ordered pairs, and as an equation.

A linear relation forms a straight line. The equation of a linear relation has a rate and a constant, and it can be represented as y=mx+b.

A function is a relation where each input produces only one output.

Function notation makes it easier to see the input and output in a function. Function notation says f(input)=output, which makes it easy to write the ordered pair (input, output), and easy to graph, since the input is on the x-axis and the output is on the y-axis.

A linear function has a graph that is a straight line. The function increases to the right if it has a positive slope (rate) and decreases if it has a negative slope (rate).

A function is non-linear if its graph is not a straight line. Some examples of non-linear functions are quadratic and cubic functions.

The vertical line test is a method for determining if a relation is a function using its graph on a coordinate plane. Imagine drawing a vertical line on the coordinate plane and scanning it from left to right. If at any point the vertical line would cross the relation in two or more places, the relation fails the vertical line test, so it is not a function.