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Math 41 Exam 1 Review
1.1 Lines in the Plane
You need to be able to find the slope of a line using two points as
reference.
2
1
2
1
2
1
,
.
y
y
m
x
x
x
x
Remember that a horizontal line has a slope of 0, and a
vertical line has an undefined slope.
You need to know the 2 forms for the equation of a
line: PointSlope Form and SlopeIntercept Form.
Which form you use depends on what
information you are given in the problem.
If you are given two points, or a point and the
slope, use PointSlope Form.
If you are given the slope and the yintercept, use Slope
Intercept Form.
You can go from PointSlope Form to SlopeIntercept Form by solving
for y.
Two lines are parallel
iff their slopes are equal.
Two lines are perpendicular
iff
their slopes are negative reciprocals of each other.
You need to be able to use this
information to write the equations of parallel or perpendicular lines to a given line
through a point.
1.2 Functions
 Recall the definition of a function: A function
f
from a set A to a set B is a
rule of correspondence that assigns to each element
x
in the set A exactly one
element y
in the set B.
The set A is the domain (or set of inputs, or set of xvalues), and the set B is
the range (or set of outputs, or set of yvalues).
We can represent functions using tables,
ordered pairs, graphs, or equations.
In functions, x is the independent variable, and y is
the dependent variable.
When using equations to represent functions, we usually use
function notation (use f(x) instead of y).
This makes it easier to plug values in for x and
f(x).
You need to be comfortable plugging in numbers, variables, and variable
expressions into functions.
You should get used to using parentheses when plugging in
values in to functions.
A piecewisedefined function is a function that has two or more
equations defined over a specified domain.
The equation that you use depends on what
xvalue you are plugging in.
One of the most important concepts in this section, and in
following sections is the concept of domain.
The implied domain is the set of all real
numbers for which the expression is defined.
You want to look to see where the function
is undefined so you can restrict your domain.
Good places to look are fractions and
radicals!
Phrase your domain so that it includes all values that make the function defined,
and then exclude values that make the function undefined.
Remember that you can have
a zero under a radical, unless it’s also in the denominator.
When in doubt, pick values in
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 Fall '07
 BRUNSDEN,VICTORW
 Math, Slope

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