5.1: Is This a Function? (Graphs)

Front

What is a function?

Back

A function is a relation that assigns exactly one output (y) for every input (x).

Front

True or False: A function can have multiple outputs for a single input.

Back

False

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

True or False: All functions are relations.

Back

True

Front

True or False: All relations are functions.

Back

False

Front

What is a relation?

Back

A relation is a set of ordered pairs, which can include functions but is not limited to them.

Front

If a graph has a curve that loops back on itself, is it a function?

Back

No, it is not a function because it fails the vertical line test.

Front

What does it mean for a graph to be a non-function?

Back

A non-function graph is one where a single input (x) can produce multiple outputs (y).

Front

Example of a function: y = 2x + 3. Is this a function?

Back

Yes, this is a function because for every x, there is exactly one y.

Front

Example of a non-function: y^2 = x. Is this a function?

Back

No, this is not a function because for some x values, there are two corresponding y values.