EVALUATE USING FUNCTION NOTATION

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

How can you determine if a relation is a function?

Back

A relation is a function if no x-values repeat; each input must correspond to only one output.

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 which the function is defined.

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

What does it mean for x-values to repeat in a relation?

Back

If x-values repeat, it means that there are multiple outputs (y-values) for the same input (x-value), which disqualifies the relation from being a function.

Front

What is the significance of the vertical line test?

Back

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

Front

How do you find the domain of a function from its graph?

Back

To find the domain from a graph, identify all the x-values that the graph covers, including any restrictions.

Front

How do you find the range of a function from its graph?

Back

To find the range from a graph, identify all the y-values that the graph covers, including any restrictions.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each x-value has a unique corresponding y-value.

Front

What is an example of a relation that is not a function?

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the x-value 1 corresponds to two different y-values.