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 = x y = -2x + 6 |
or or |
f(x) = x f(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:
• 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.
• If A ≠
0, then the range is all real numbers, (-∞,
+∞).
• 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.
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