Understanding functions

Front

What is a function?

Back

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

Front

What does it mean if a relation is not a function?

Back

A relation is not a function if at least one input (x-value) is associated with more than one output (y-value).

Front

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

Back

Check if any x-value is repeated with different y-values. If so, it is not a function.

Front

What is the vertical line test?

Back

The vertical line test states that if a vertical line intersects a graph at more than one point, the graph does not represent a function.

Front

Given the ordered pairs {(1,2), (2,3), (1,4)}, is this a function?

Back

No, because the x-value 1 has two different y-values (2 and 4).

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input has only one output.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b.

Front

What is a quadratic function?

Back

A quadratic function is a function that can be expressed in the form y = ax^2 + bx + c, where a ≠ 0.