Identifying Functions From Various Representations

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If a vertical line intersects the curve at more than one point, it is not a function.

Front

What does it mean for a graph to represent a function?

Back

A graph represents a function if every x-value (input) has exactly one corresponding y-value (output).

Front

Identify a function from a set of ordered pairs: {(1,2), (2,3), (3,4), (1,5)}

Back

This set is not a function because the input '1' corresponds to two different outputs (2 and 5).

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is related to exactly one input, meaning no two different inputs produce the same 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, where m is the slope and b is the y-intercept.

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, b, and c are constants and a ≠ 0.

Front

How can you tell if a graph is not a function?

Back

A graph is not a function if any vertical line drawn through the graph intersects it at more than one point.

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions for different intervals of the input.

Front

What is the domain of a function?

Back

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