College Algebra, October 22, 2012
Section 4.4
The Remainder Theorem tells us that we can find the value of f(c) by doing the
synthetic division of f(x) by (x-c) and noticing that the remainder is f(c). Sometimes this
is faster than substituting c for x in
If h is positive, and if the graph of f is known,
The graph of
f ( x + h)
The graph of
f ( x ) + h is the graph of f(x) shifted h units up.
is the graph of f(x) shifted h units to the left.
Example: Write an equation for a function g(x) that is similar to
College Algebra
October 19, 2012
4.3 (Continued)
Piecewise-Defined Functions:
Many real-world situations are best modeled by this type of function, because the
function is very different on different sections of the domain.
Example:
x if x < 4
f ( x) = 2
The domain of a rational function includes all real numbers
except the zeros of the denominator q(x).
The graph of a rational function is continuous except at xvalues where
q(x) = 0.
The line x = k is a vertical asymptote of the graph of f if f(x)
or f(x)
Test 2
_
1) Vertex, axis of symmetry of quadratic function
2) Quadratic Inequalities
3) Domain of quad.
4) Quad problem Solving
5)x-intercepts of polynomial fns.
6) multiplicity of zeros & how the graph
looks
3.4 Quadratic Inequalities
Three different concepts that are closely related:
Quadratic Function:
Quadratic Equation:
Quadratic Inequality:
The Graphical Basis for Our Method:
Solving Quadratic Inequalities Graphically:
The Algebraic Method of Solving Qua
3.4 Quadratic Inequalities
Three different concepts that are closely related:
Quadratic Function:
Quadratic Equation:
Quadratic Inequality:
The Graphical Basis for Our Method:
Solving Quadratic Inequalities Graphically:
The Algebraic Method of Solving Qua
MATH
1130
COLLEGE ALGEBRA
Study Guide 10
Section 1.2
o Know the difference between the sort of statistical analysis
that can be performed on on-variable data (most commonly
measures of average such as mean and median), compared
to the wider range that can
MATH
1130
COLLEGE ALGEBRA
Study Guide 9
Section 1.1
o Know the difference between the different types of numbers
used in this course (natural numbers, whole numbers,
integers, rational numbers, irrational numbers, real numbers,
complex numbers)
o Be famil