Pre- calculus
Properties of lines

Slope The slope m of the line through the
points (x1, y1) and (x 2, y 2) is given by

Point slope :The straight-line equations is
called the "point-slope" y – y1 = m(x – x1)
12 basic functions and graphs
the twelve functions Identity Function, Squaring function, Cubing Function, Square Root Function,
Reciprocal Function, Exponential Function, Natural Logarithm Function, Sine Function, Cosine Function and
the Logistic Function
Cont…
Some of the best ways to describe the
functions are the following .

domain: the set of the values were
we take the x values,

continuous: were every point in the
graph as a value

bounded: the graph lies in two
horizontal lines

(A graph can be bounded above or
below or completely bounded.)

even: the function of the graph will
be symmetric with the y-axis

odd: the main function of the graph
will always be symmetric with its
origin

increasing: the graph is going
upward as it moves from left to right

decreasing: the function's is going
downward as it moves from left to
right
oTRANSFORMATIONS
The different types of transformations
are the following:
- Translation
- Reflection
- Point Reflection
- Rotation
- Dilation
 A trabsformation is just a moving shape that
will have a different position as the original
one ,but still stay with the same size, area,
angles, and line lengths
The following formulas well help
you solve for the shifts, reflection,
transformation, vertical shift and
all that good stuff.
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VERTICAL AND HORIZONTAL SHIFTS
Suppose c > 0 . To obtain the graph of
y = f (x) + c : shift the graph of y = f (x) up by c units
y = f (x) − c : shift the graph of y = f (x) down by c units
y = f (x − c) : shift the graph of y = f (x) to the right by c units
y = f (x + c) : shift the graph of y = f (x) to the left by c units
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REFLECTIONS
To obtain the graph of
y = − f (x) : reflect the graph of y = f (x)
about the x-axis
y = f (−x) : reflect the graph of y = f (x) about
the y-axis
Example
#1
 Example from purple math For
F(t) = Af(Bt – C)+D, where f(t) is one of the
basic trig functions, we have:
 A: amplitude is A
 B: period is (2π)/|B|
 C: phase shift is C/B
 D: vertical shift is D

This is an example of a vertical strach graph from
Pearson's calculus website