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Unformatted text preview: The domain of a constant function is (−∞, ∞).
Recall that to graph a function, f , we graph the equation y = f (x). Hence, the graph of a linear
function is a line with slope m and y -intercept (0, b); the graph of a constant function is a horizontal
line (with slope m = 0) and a y -intercept of (0, b). Now think back to Section 1.7.1, speciﬁcally
Deﬁnition 1.8 concerning increasing, decreasing and constant functions. A line with positive slope
was called an increasing line because a linear function with m > 0 is an increasing function.
Similarly, a line with a negative slope was called a decreasing line because a linear function with
m < 0 is a decreasing function. And horizontal lines were called constant because, well, we hope
you’ve already made the connection.
Example 2.1.4. Graph the following functions. Identify the slope and y -intercept.
1. f (x) = 3 3. f (x) = 3 − 2x
4 2. f (x) = 3x − 1 4. f (x) = x2 − 4
1. To graph f (x) = 3, we graph y = 3. This is a horizontal line (m = 0) through (0, 3).
2. The graph of f (x) = 3x − 1 i...
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