Linear vs Non-Linear 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 non-linear function?

Back

A non-linear function is a function that does not form a straight line when graphed. It can include quadratic, exponential, and other types of functions.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear function?

Back

The slope (m) represents the rate of change of the function; it indicates how much y changes for a unit change in x.

Front

What does the y-intercept (b) represent in a linear function?

Back

The y-intercept (b) is the point where the line crosses the y-axis, indicating the value of y when x is 0.

Front

Give an example of a linear function.

Back

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

Front

Give an example of a non-linear function.

Back

An example of a non-linear function is y = x^2.

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.

Front

How can you identify a non-linear function from its graph?

Back

A non-linear function can be identified by its curved graph, which does not have a constant slope.

Front

What is the difference between a function and a non-function?

Back

A function assigns exactly one output for each input, while a non-function may assign multiple outputs for a single input.