Identifying Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input.

Front

What does it mean for a function to be linear?

Back

A linear function is a function whose graph is a straight line, which can be expressed in the form y = mx + b.

Front

What does it mean for a function to be nonlinear?

Back

A nonlinear function is a function whose graph is not a straight line, meaning it does not have a constant rate of change.

Front

How can you identify a linear function from a table of values?

Back

If the differences between consecutive y-values are constant for equal intervals of x-values, the function is linear.

Front

How can you identify a nonlinear function from a table of values?

Back

If the differences between consecutive y-values are not constant for equal intervals of x-values, the function is nonlinear.

Front

What is the slope of a linear function?

Back

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

Front

Can a function have more than one output for a single input?

Back

No, a function cannot have more than one output for a single input; this is a key characteristic of functions.

Front

What is an example of a linear function?

Back

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

Front

What is an example of a nonlinear function?

Back

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