4-3 Linear vs. Non-Linear Functions

Front

What is a function?

Back

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

Front

What is the definition of 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 nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line and may include curves, bends, or other shapes.

Front

How can you determine if a table of values represents a function?

Back

A table represents a function if each input value corresponds to exactly one output value.

Front

What does it mean if a function has more than one output for a single input?

Back

If a function has more than one output for a single input, it is not a function.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the rate of change of y with respect to x, represented by 'm' in the equation y = mx + b.

Front

What is the y-intercept in a linear function?

Back

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

Front

What is the difference between a linear and a nonlinear graph?

Back

A linear graph is a straight line, while a nonlinear graph can be curved or have varying slopes.

Front

Can a function be both linear and nonlinear?

Back

No, a function cannot be both linear and nonlinear; it must fit one definition or the other.

Front

What is an example of a linear function?

Back

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