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Unformatted text preview: e function.
Two cases where f (x ) may not be deﬁned as a real number
are:
1
2 Points x for which division by zero occurs.
Points x for which a negative even root occurs. Outline Functions Representing Functions The Domain and Range Evaluating Functions Examples Example
Find the domain and range of each of the following.
1 f (x ) = x 2 2 f (x ) = 3 x
.
−4
√
f (x ) = 3x − 1.
x2 Average Rate of Change Outline Functions Representing Functions The Domain and Range Evaluating Functions Average Rate of Change Evaluating a Function Let f : D → Y be a function.
We evaluate f at a point x = c if we replace all variables x in
the expression for f (x ) by the number c .
The output is denoted y = f (c ).
Example
Evaluate the function f (x ) = 3x 2 − 4x at x = 0, −1, 1, 2, 2c , c + 1. Outline Functions Representing Functions The Domain and Range Evaluating Functions Average Rate of Change The Average Rate of Change of a Function Deﬁnition
Suppose f is a function that is continuous on an interval [a, b ].
The average rate of change of f on [a, b ] is the number
∆y
f (b ) − f (a)
=
.
∆x
b−a
This is the slope of the secant line that goes through the points
(a, f (a)) and (b , f (b )).
Example
#102 in the book....
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 Spring '14
 K.JPlatt
 Algebra, Rate Of Change

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