Compound Inequalities A compound Inequality is when you have your variable is compared to two...

Compound Inequalities•A compound Inequality is when you have your variable is compared to two different values.

•There are two ways that you will see compound inequalities written.

a) -2 < x < 1This is read, “x is greater

than -2 AND less than 1.”

•“AND” means that the variable is in-between the solutions, which means that your graph will be colored between the dots

•This will always be the case when the inequality symbols are facing in the same direction.

Compound Inequalitiesb) x < -1 or x > 2

This is read, “x is less than -1 OR greater

than 2.”

•“OR” means that you have two separate inequalities therefore graph will have arrows facing different directions.

•This will always be the case when the inequality symbols are facing different directions.

Absolute

Value

Definition: The distance a number is from zero on a number line

The symbol for absolute value is two vertical line surrounding the number or expression.

Treat the vertical lines as if they are parenthesis and solve everything in them before moving on to any other part of the expression.

Which point has the greatest absolute value?

Which point has the least absolute value?

To solve an absolute value equation…

1) set the equation equal to the solution given and solve.

2) then set the equation equal to the opposite of the solution and solve.

examples: pg 53 # 20-22pg 53 # 26-28

FunctionsVocabulary Terms to Know:

DOMAIN: All of the “x” values

RANGE: All of the “y” values

RELATION: any set of ordered pairs… ex: (3,8)

FUNTION: When there is exactly one output for every input. In other words for every “x” there has to be a unique “y”. A function will pass the Vertical Line Test.

Is It a Function?To determine if an equation is a function you have two options…

OPTION #1: Graph the equation and see if it passes the vertical line test. To pass the vertical line test you must be able to draw a vertical line anywhere on the graph and it will only intersect (touch) the graph in one location. If it touches in more than one location, it is NOT a function.

Examples: pg 72 #25-27

Is It a Function?To determine if an equation is a function you have two options…

OPTION #2: Look at the “x” and “y” values provided. If a number appears in the “x” column more than once and the corresponding “y” value is not the same both times, it is NOT a function

Examples: pg 71 #22-24

SlopeVocabulary Terms to Know:

Slope: The ratio of the vertical change of a line to the horizontal change of the same line

~ “Rise over the Run” is a phrase often used to describe slope. This means the vertical change over the horizontal change.

~ The formula for slope is y2 – y1

x2 – x1

Slope~ If the line falls from left to right then

the slope of the line is negative.

~ If the line rises from left to right then the slope of the line is positive.

~ If the line is a horizontal line is has a slope of zero.

~ If the line is a vertical line it has a slope that is undefined. This is because when you find the difference of the two “x” coordinates, your denominator will be zero.

Examples: pg 79 # 4 – 9

pg 79 #17 – 19

Positive, Negative, Zero, or Undefined?

Positive, Negative, Zero, or Undefined?

Positive, Negative, Zero, or Undefined?

Positive, Negative, Zero, or Undefined?

SlopeVocabulary Terms to Know:

Parallel: Two lines that are always the same distance apart. If two lines are parallel they will have equivalent slopes.

Perpendicular: Two lines that intersect to form a right (90°) angle.

If two lines are perpendicular their slopes are negative reciprocals.

Examples: pg 79 #12 – 15

Graphs of Linear Equations

•A line in the form x = ? is a vertical line.•A line in the form y = _?_ is a horizontal line

Slope Intercept Form:

y = mx + b

m represents the slope of the line (the numerator is the vertical change and the denominator is the horizontal change)

b represents the y-intercept of the line (where the line crosses the y-axis)

Graphs of Linear Equations

To draw a line given an equation in slope intercept form…

• write the equation in slope intercept form by solving for y.

• plot the y-intercept first by counting up or down the y-axis

• count up (if the slope is positive) or down (if the slope is negative) based on the number in the numerator of the slope

• count to the right based on the number in the denominator of the slope

• connect the two points using a straightedge

Examples: pg 86 #4 – 6 (verbal) 10 - 15 (graph them), 16 – 18 (verbal), 19, 22 – 24 (graph them)

Homework: pg 87 #37-39, 43-47, 49, & 50

Graphs of Linear Equations

There are several situations that you will face when asked to write the equation of a line…

1)Given the slope and the y intercept use SLOPE-INTERCEPT FORM: y = mx + b

ex: pg 95 #4 & 5

2) Given the slope and a point use POINT-SLOPE FORM: y- y1 = m (x – x1)

ex: pg 95 #6 & 7

Graphs of Linear EquationsGiven a point and the equation of

another line that is either parallel or perpendicular to the line in question:

1) Use the equation of the line given to find the slope of the line you are trying to write an equation for.

parallel = same slope

perpendicular = negative reciprocal

2) Use the slope found in the previous step and one of the points given to fins the equation of the using POINT-SLOPE FORM

ex: pg 95 #10 & 11

Graphs of Linear Equations3) Given two points…

a) find the slope using the slope formulab) use the slope found in the previous step and one of the points given to fins the equation of the using POINT-SLOPE FORM

ex: pg 95 #8 & 9

Your turn: pg 95 #13 – 15, 19 – 21, 25 – 27, 35 – 37

HW: pg 95 #16 , 17, 22, 23, 27, 28, 38, 39

Test Review1) Solve the equation:

2) Solve and graph the solution:

3) Find the equation of a line that contains the point (6,2) and is parallel to the line 2y = 3x – 6

9

2

9

4

6

1

3

2 xx

532 x or 974 x

Test Review4) Are the following lines parallel, perpendicular, or

neither?

line1: 2y = 5x + 6

line 2: 5y + 2x = 10

5) What is the domain and range of the graph below?

6) Is the graph to the left a function? Why or why not?

Test Review7) Which chart(s) below do not represent a function?

X Y

0 1

1 2

2 3

3 3

X Y

0 1

1 2

1 3

3 3

X Y

0 1

1 2

2 3

2 3

Test Review8) What is the equation of the line?