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# Chapter 1

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by

## Megan Fitch

on 15 December 2014

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#### Transcript of Chapter 1

Chapter 2
Chapter 3
What makes a graph a function
You can tell if a graph is a function by using the vertical line test. If the graph is a function, then it should never cross the vertical line more than once.

Chapter 4
linear equation
the value of one of the variables depends on the value of the other variable. X is the independent variable and y is the dependent variable.
Weeee Math
MATH
ex.
y=2x+1
x represents an unknown, and a, b, and c represent numbers
ex. x^2+4-4=0
3 ways to solve a quadratic equation
way 1: factoring equations
ex. x 2 - 5x - 14 = 0
(x - 7)(x + 2) = 0
x - 7 = 0 or x + 2 = 0
x = 7 or x = - 2
ex.
way 3: completing the square
ex. 4x^2-2x-5=0
4x^2-2x=5
rearrange the quadratic into the neat "(squared part) equals (a number)" format. remember that finding the x-intercepts means setting y equal to zero and solving for the x-values
graphing and solving inequalities
graphing inequalities
•if the symbol is or
then you fill in the dot, like the top two examples in the graph below
•if the symbol is (> or <) then you do not fill in the dot like the bottom two examples in the graph below

ex. x<3

solving inequalities
most linear inequalities can be solved just the same as linear equations. Addition and subtraction of any number (positive or negative) can be done to the expression on either side of the inequality without changing the inequality itself.
ex.
solving an absolute value equation
use the positive/negative property of the absolute value to split the equation into two cases

ex.
Solve | x + 2 | = 7
To clear the absolute value bars, I must split the equation into its two possible two cases, one case for each sign:
(x + 2) = 7 or –(x + 2) = 7
x + 2 = 7 or –x – 2 = 7
x = 5 or –9 = x
Then the solution is x = –9, 5.

you "solve" equations by "isolating" the variable; you isolate the variable by "undoing" whatever had been done to it. When you have a variable inside a square root, you undo the root by doing the opposite: squaring. For instance, given , you would square both sides.

ex.

Chapter 1
How do you find the domain OF an equation
The domain of an equation is simply the x-values
What transformations can be done on graphs?
Function
f (x)+c
f (x)-c
f (x+c)
f(x-c)
-f(x)
f(-x)
a*f(x), a>1
a*f(x), 0<a<1
f(ax), a>1
f(ax), 0<a<1

Transformation of the graph of f (x)
Shift f ( x) upward c units
Shift f ( x) downward c units
Shift f ( x) to the left c units
Shift f ( x) to the right c units
Reflect f ( x) in the x-axis
Reflect f ( x) in the y-axis
Stretch f ( x) vertically by a factor of a.
Shrink f ( x) vertically by a factor of a.
Shrink f ( x) horizontally by a factor of 1/a
Stretch f ( x) horizontally by a factor of 1/a
How do you find min/max points from vertex and standard form?
The vertex is just (h,k) from the equation.
The x-coordinate of the vertex can be found by the formula -b2a, and to get the y value of the vertex, just substitute -b2a, into the x

How do you find distance and midpoint?
How to find intercepts of a graph
X Intercept: where the graph of an equation crosses the x-axis.

Y Intercept: where the graph of an equation crosses the y-axis.
what are 3 main types of symmetry from a graph
symmetric about the x-axis if whenever is on the graph then so is . Here is a sketch of a graph that is symmetric about the x-axis.
A graph is said to be symmetric about the y-axis if whenever is on the graph then so is
. Here is a sketch of a graph that is symmetric about the y-axis.

A graph is said to be symmetric about the origin if whenever
is on the graph then so is .
Here is a sketch of a graph that is symmetric about the origin.
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