Linear and Non Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, characterized by a constant rate of change.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line, and its rate of change is not constant.

Front

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

Back

If the differences between consecutive outputs (y-values) are constant for equal differences in inputs (x-values), the function is linear.

Front

What is the rate of change in a linear function?

Back

The rate of change is the slope of the line, representing how much the output (y) changes for a unit change in the input (x).

Front

What is the formula for the slope of a line?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What does it mean for a function to have a constant slope?

Back

A constant slope means that the rate of change between the input and output values remains the same throughout the function.

Front

What is the definition of a function?

Back

A function is a relation where each input has exactly one output.

Front

What is an example of a linear function in real life?

Back

An example is the cost of a meal that includes a fixed delivery fee plus a cost per person.

Front

What is an example of a nonlinear function in real life?

Back

An example is the area of a circle as a function of its radius, which is A = πr².

Front

How do you determine if a function is linear or nonlinear from a graph?

Back

If the graph is a straight line, it is linear; if it curves or has bends, it is nonlinear.