Functions, Functions, Functions

Front

What is a function in mathematics?

Back

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

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for that function.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How can you determine if a table represents a function?

Back

A table represents a function if each x-value is unique; no x-value should repeat.

Front

What does it mean if a graph is a function?

Back

A graph is a function if it passes the vertical line test, meaning no vertical line intersects the graph at more than one point.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function by checking if any vertical line crosses the graph more than once.

Front

What is an example of a non-function?

Back

An example of a non-function is the relation {(1,2), (1,3)}, where the x-value 1 is associated with two different y-values.

Front

What is the significance of unique x-values in a function?

Back

Unique x-values ensure that each input has a single output, which is a defining characteristic of functions.

Front

For the function {(0,1), (1,-3), (2,-4), (-4,1)}, what is the domain?

Back

The domain is {0, 1, 2, -4}.

Front

For the function {(0,1), (1,-3), (2,-4), (-4,1)}, what is the range?

Back

The range is {1, -3, -4}.