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 Dependent Variable

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# Linear Functions

You have learned that a function is a rule that assigns to each input number, x, exactly one output number, y.

A linear function is a rule that can be written in the form:

y = Ax + B or f(x) = Ax + B

For example, the following are linear functions:

 y = xy = -2x + 6 oror f(x) = xf(x) = -2x + 6

The following functions are not linear functions:

y = x2 - 7 or f(x) = x2 - 7 (Not linear since x is squared.)

(Not linear since x is in the denominator.)

For any linear function y = Ax + B:

â€¢ The domain is all real numbers, which is the interval (-, +).

This is because we can multiply any input x, by any real number A, and then add any real number B.

â€¢ If A 0, then the range is all real numbers, (-, +).

â€¢ If A = 0, then the graph is a horizontal line. In that case, the range is the single number B.

In applications of linear functions, however, the domain and range may be restricted to only a portion of the real numbers.