Linear vs Non-Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line. It has the form f(x) = 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 create a straight line when graphed. It can include quadratic, exponential, logarithmic, and other types of functions.

Front

Identify the general form of a linear equation.

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Front

What does it mean for a function to be quadratic?

Back

A quadratic function is a type of non-linear function that can be expressed in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How can you identify a non-linear equation?

Back

You can identify a non-linear equation by looking for exponents greater than one, variables multiplied together, or functions like sine, cosine, or exponential.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of the function when x = 0.

Front

Give an example of a linear function.

Back

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

Front

Give an example of a non-linear function.

Back

An example of a non-linear function is f(x) = x² - 4.

Front

What is the difference between a linear and a non-linear graph?

Back

A linear graph is a straight line, while a non-linear graph can be curved or have various shapes.