Functions

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 notation for a function?

Back

The notation for a function is typically f(x), where 'f' is the name of the function and 'x' is the input variable.

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be graphically represented as a straight line, which means it has the form f(x) = mx + b, where m and b are constants.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in the y-value to the change in the x-value, often represented as 'm' in the equation y = mx + b.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of 'b' in the equation y = mx + b.

Front

How do you find the value of a function at a specific point?

Back

To find the value of a function at a specific point, substitute the input value into the function's equation.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while nonlinear functions do not have a constant rate of change and can graph as curves.

Front

What is an example of a linear function?

Back

An example of a linear function is y = 2x + 3.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if each output is produced by exactly one input, meaning no two different inputs produce the same output.