Identify Functions #1

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 used to determine if a curve is a graph of a function. If any vertical line intersects the graph at more than one point, then the graph is not a function.

Front

What is the domain of a function?

Back

The domain of a function is the complete set of possible values of the independent variable (input) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the complete set of possible values of the dependent variable (output) that result from using the function.

Front

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

Back

A relation is not a function if at least one input is related to more than one output.

Front

Give an example of a function.

Back

An example of a function is f(x) = 2x + 3, where for every value of x, there is exactly one corresponding value of f(x).

Front

Give an example of a relation that is not a function.

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the input 1 is related to two different outputs.

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 can be graphically represented as a straight line, typically in the form f(x) = 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 f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.