Is it a Function? & Describe Graphs

Front

What is a function?

Back

A function is a relation where every input (x-value) has exactly one output (y-value).

Front

Which of the following sets is not a function? (3,4) (4,-3) (7,4) (3,8)

Back

This set is not a function because the input '3' has two different outputs: '4' and '8'.

Front

What does it mean for a relation to be a function?

Back

It means that for every input, there is only one corresponding output.

Front

What is the definition of a relation?

Back

A relation is a set of ordered pairs, where each pair consists of an input and an output.

Front

How can you determine if a set of points is a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What does the vertical line test indicate?

Back

If a vertical line crosses a graph more than once, the graph does not represent a function.

Front

What happens to the graph of a function as you move from left to right?

Back

The graph may increase, decrease, or remain constant, but each x-value must have only one y-value.

Front

What is an example of a function?

Back

The equation y = 2x + 3 is a function because for every x-value, there is one y-value.

Front

What is an example of a non-function?

Back

The equation x^2 + y^2 = 1 is not a function because it can produce multiple y-values for a single x-value.

Front

What does it mean for a graph to be increasing?

Back

A graph is increasing if, as you move from left to right, the y-values rise.