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. It can include quadratic, exponential, logarithmic, and other types of functions.

Front

What is the definition of a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

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.

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What is the slope of a linear function?

Back

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

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What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the graph intersects the y-axis, represented by the value of b in the equation f(x) = mx + b.

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What is an example of a nonlinear function?

Back

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

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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 exists at least one input that is associated with more than one output.

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How can you determine if a relation is a function using the vertical line test?

Back

The vertical line test states that if a vertical line intersects the graph of a relation at more than one point, then the relation is not a function.

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What is the general form of a quadratic function?

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The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.