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 f(x) = mx + b, where m is the slope and b is the y-intercept.

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What is a Nonlinear Function?

Back

A nonlinear function is a function that does not form a straight line when graphed. Its graph can be a curve, a circle, or any other shape that is not linear.

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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 outputs for a single input. This violates the definition of a function, which states that each input must have exactly one output.

Front

Give an example of a Linear Function.

Back

An example of a linear function is f(x) = 2x + 3. Its graph is a straight line with a slope of 2 and a y-intercept of 3.

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Give an example of a Nonlinear Function.

Back

An example of a nonlinear function is f(x) = x^2. Its graph is a parabola, which is not a straight line.

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What is the slope in a linear function?

Back

The slope (m) in a linear function represents the rate of change of the function. It indicates how much the output (y) changes for a unit change in the input (x).

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What is the y-intercept in a linear function?

Back

The y-intercept (b) in a linear function is the point where the graph intersects the y-axis. It represents the value of the function when x = 0.

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How can you identify a Linear Function from a table of values?

Back

A linear function will have a constant rate of change between the x-values and y-values. If the differences in y-values divided by the differences in x-values are constant, it is linear.

Front

How can you identify a Nonlinear Function from a table of values?

Back

A nonlinear function will show varying rates of change between the x-values and y-values. If the differences in y-values divided by the differences in x-values are not constant, it is nonlinear.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.