Linear Vs. Nonlinear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has 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 form a straight line when graphed. Its rate of change is not constant, and it can take various forms such as quadratic, exponential, or logarithmic.

Front

How can you identify a linear function from its graph?

Back

A linear function can be identified by its straight line graph, which has a constant slope and does not curve.

Front

How can you identify a nonlinear function from its graph?

Back

A nonlinear function can be identified by its curved graph, which does not have a constant slope and may change direction.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the input values (x) increase, the output values (y) also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the input values (x) increase, the output values (y) decrease.

Front

What does it mean for a function to be both increasing and decreasing?

Back

A function is both increasing and decreasing if it has sections where it rises and sections where it falls, indicating a change in direction.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

What is the y-intercept of a linear function?

Back

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

Front

Can a nonlinear function have a constant rate of change?

Back

No, a nonlinear function does not have a constant rate of change; its slope varies at different points.