Identifying Functions and Function Tables

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 vertical line test?

Back

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

Front

What does it mean for a relation to have repeated x-values?

Back

A relation has repeated x-values if the same input (x-value) is paired with different outputs (y-values), which means it cannot be classified as a function.

Front

Can a function have the same y-value for different x-values?

Back

Yes, a function can have the same y-value for different x-values, as long as each x-value is paired with only one y-value.

Front

What is a mapping in the context of functions?

Back

A mapping is a way to describe how each element in a set (domain) is paired with an element in another set (range). It can be represented using arrows or ordered pairs.

Front

What is the definition of a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x-value) and an output (y-value).

Front

How can you determine if a graph represents a function?

Back

You can determine if a graph represents a function by using the vertical line test. If any vertical line crosses the graph more than once, it is not a function.

Front

What is an example of a non-function relation?

Back

An example of a non-function relation is {(1, 2), (1, 3), (2, 4)}, where the x-value 1 is paired 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 corresponds to exactly one output, which is a fundamental property of functions.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if each output (y-value) is paired with exactly one input (x-value), meaning no two different x-values can produce the same y-value.