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

quadratic equation

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

way 2: use quadratic formula

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.

solving equations with a radical

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.