TEKS 8.5G

Front

What is a function?

Back

A function is a relation between a set of inputs (x-values) and a set of possible outputs (y-values) where each input is related to exactly one output.

Front

How can you determine if a set of ordered pairs represents y as a function of x?

Back

A set of ordered pairs represents y as a function of x if no two pairs have the same x-value with different y-values.

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, then the graph does not represent a function.

Front

What does it mean for y to be a function of x?

Back

It means that for every value of x, there is exactly one corresponding value of y.

Front

What is an example of a function?

Back

An example of a function is the equation y = 2x + 3, where each x-value has a unique 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 the set of ordered pairs {(1, 2), (1, 3)}, where the x-value 1 corresponds to two different y-values.

Front

What is the definition of an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) where x is the first element and y is the second element, representing a point in a coordinate system.

Front

What does it mean for a mapping to represent y as a function of x?

Back

It means that each x-value in the mapping corresponds to exactly one y-value.

Front

What is the difference between a function and a non-function?

Back

A function has a unique output for each input, while a non-function may have multiple outputs for a single input.

Front

How can you identify a function from a graph?

Back

You can identify a function from a graph by using the vertical line test; if any vertical line crosses the graph more than once, it is not a function.