Unformatted text preview: is called the leading coefficient.
The domain of any polynomial function is all real numbers. Definition of a function: A function is a rule that assigns to
each element in one set exactly one element from another set.
In other words, for each input (independent variable) there is
exactly one output (dependent variable).
Definition of domain: The domain of a function is the set of
all possible real values for the independent variable (or in
other words, the set of all allowable values, or meaningful
replacements for x).
Definition of range: The resulting set of all possible output values for the dependent variable (or y) is called the range. 2. Rational Functions
Rational functions are so named because they are a ratio of
Rational functions are functions of the form f (x) =
where p(x) and q(x) are polynomials and q(x) Z 0. Quadratic Functions Quadratic functions: f1x2 = ax 2 + bx + c, where a, b, and
c are real numbers and a Z 0.
Properties of quadratic functions:
1. If a 7 0, the parabola opens up. If a 6 0, the parabola
2. Parabolas have either a highest or lowest point. This point
is called the vertex. Asymptotes: If a function grows without bound as x
approaches some number k, then x = k is a vertical
To find vertical asymptotes for rational functions:
Set the denominator equal to 0 and solve for x. -b
The x-coordinate of the vertex is x =
, and the
corresponding y-coordinate is f a
b . (Find the value
5. Range: ( - q , q ) 1 ISBN 0-321-37440-1 x:a x:a x:a lim 3 f (x) # g (x)4 = C lim f (x) D x:a x:a lim B x:a x:a # C lim g (x) D
2. = A#B lim f (x)
= , B Z 0.
B 3. x:a 6. log a a r = r 7. a loga x If p(x) is a polynomial, then lim p(x) = p(a). 4. 7. log a 1 = 0 For any real number k, lim C f (x) D k = C lim f (x) D k = Ak, 5. x:a x:a x:a provided this limit exists. =x 8.
9. SPECIAL NOTATIONS The common log: log 10 x Q log x
The natural log: log e x Q ln x lim f (x) = lim g(x) if f (x) = g(x), for all x Z a. x:a x:a For any real number b, b 7 0, lim b
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- Spring '09