"Function or Not a Function" Flashcard

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

How can you determine if a relation is a function using a table?

Back

A relation is a function if no x-value is repeated with different y-values in the table.

Front

What does the vertical line test determine?

Back

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

Front

Is the equation y^2 = x + 4 a function?

Back

No, because for some x-values, there are two corresponding y-values (positive and negative).

Front

Is the equation y = x^2 + 5 a function?

Back

Yes, because each x-value has exactly one corresponding y-value.

Front

What is the definition of a relation?

Back

A relation is a set of ordered pairs (x, y) that shows a relationship between x and y.

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, but each input must have only one output.

Front

What is an example of a non-function?

Back

The relation {(1, 2), (1, 3)} is not a function because the input 1 has two different outputs.

Front

What is an example of a function?

Back

The relation {(1, 2), (2, 3), (3, 4)} is a function because each input has a unique output.

Front

What is the importance of functions in mathematics?

Back

Functions are important because they describe relationships between quantities and are used in various applications in science, engineering, and economics.