Linear and 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. It can have curves, bends, or other shapes, and can be represented by equations like y = ax^2 + bx + c.

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What does it mean for a relation to be 'Not a Function'?

Back

A relation is 'not a function' if there are two or more inputs (x-values) that produce the same output (y-value). This violates the definition of a function.

Front

Identify if the following is linear or nonlinear: y = 7x^3 + 5

Back

Nonlinear

Front

Identify if the following is linear or nonlinear: y = 4x + 6

Back

Linear

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 is the slope in a linear function?

Back

The slope (m) in a linear function represents the rate of change of y with respect to x. It indicates how steep the line is.

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What is the y-intercept in a linear function?

Back

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

Front

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

Back

A table represents a linear function if the differences between consecutive y-values are constant when the x-values increase by the same amount.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which represents a parabola.