Determining Functions

Front

What is a linear equation?

Back

An equation that graphs to a straight line, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear equation?

Back

An equation that does not graph to a straight line, which can include curves, circles, or other shapes.

Front

What is a function?

Back

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

Front

What is the vertical line test?

Back

A method to determine if a relation is a function; if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is a domain in a function?

Back

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

Front

What is a range in a function?

Back

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

Front

What does it mean for a relation to be not a function?

Back

A relation where at least one input (x-value) corresponds to more than one output (y-value).

Front

Give an example of a linear function.

Back

f(x) = 2x + 3 is a linear function.

Front

Give an example of a nonlinear function.

Back

f(x) = x^2 is a nonlinear function.

Front

What is a one-to-one function?

Back

A function where each output is paired with exactly one input, meaning no two different inputs produce the same output.