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. 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 equation?

Back

If the equation can be expressed in the form y = mx + b, where m and b are constants, it is a linear function.

Front

What does the slope of a linear function represent?

Back

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

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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, representing the value of y when x = 0.

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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.

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What is an example of a linear function?

Back

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

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What is an example of a non-linear function?

Back

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

Front

How can you tell if a graph represents a linear function?

Back

A graph represents a linear function if it forms a straight line.

Front

What does it mean if a graph is nonlinear?

Back

If a graph is nonlinear, it means that the relationship between the variables is not constant and the graph does not form a straight line.