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CHAPTER 4

Vobcabulary

Compound Inequalities- two inequalities that are joined by and or or

5 < x and x < 10

14 < x or x ≥ -3

Equivalent Inequalities- equivalent inequalities have the same set of solutions

x + 4 < 7 and x < 3 are equivalent inequalities

Solution of an Inequality (one variable)- any value or values of a variable in the inequality that makes an inequality true

The solution of the inequality x < 9 is all numbers less than 9

Properties and Formulas

Properties of Inequality

Addition

if a > b, then a + c > b + c

3 > 1, so 3 + 2 > 1 + 2

if a < b, then a + c < b + c

-5 < 4, so -5 + 2 < 4 + 2

Subtraction

if a > b, then a - c > b - c

3 > -1, so 3 - 2 > -1 - 2

if a < b, then a - c < b - c

-5 < 4, so -5 - 2 < 4 - 2

Multiplication

if c > 0

if a > b, then ac > bc

4 > -1, so 4(5) > -1(5)

if a < b, then ac < bc

-6 < 3, so -6(5) < 3(5)

if c < 0

if a > b, then ac < bc

4 > -1, so 4(-2) < -1(-2)

if a < b, then ac > bc

-6 < 3, so -6(-2) < 3(-2)

Division

if c > 0

if a > b, then a/c > b/c

6 > 4, so 6/2 > 4/2

if a < b, then a/c < b/c

2 < 8, so 2/2 < 8/2

if c < 0

if a > b, then a/c < b/c

6 > 4, so 6/-2 < 4/-2

if a < b, then a/c > b/c

2 < 8, so 2/-2 > 8/-2

Absolute Values

Solving Absolute Value Equations

To solve an equation in the form of |A|= b, where A represents a variable expression and b > 0, solve A = b and A = -b

|2p + 5|= 11

2p + 5 = 11

2p + 5 = -11

Solving Absolute Value Inequalities

Similar rules are true for |A|≥ b or |A|≤ b.

To solve an inequality in the form of |A|< b, where A is a variable expression and b > 0, solve -b < A < b

|n - 1| < 3

-3 < n - 1 < 3

To solve an inequality in the form of |A|> b, where A is a variable expression and b > 0, solve A < -b or A > b

|n - 1| > 3

n - 1 < 3 or n - 1 > 3

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CHAPTER 5

Vocabulary

Relation- any set of ordered pairs

{(0,0), (2,3), (2,-7)}

Vertical-Line Test- a method used to determine if a relation is a function or not. If a vertical line oasses through a graph more than once, the graph is not the of graph of the function.

*

Function Notation- to write a rule in function notation, you use the symbol f(x) in the place of y

f(x) = 3x - 8

Continuous Data- data where numbers between any two data values have meaning

temperature, length or weight

Disrcrete Data- data that involve a count of items

number of people or number of cars

Direct Variation- a linear function that can be expressed in the form y = kx or y/x = k, where k ≠ 0

y = 18x

Constant of Variation for Direct Variation- the nonzero constant k in the function y = kx

for the function y = 24x, 24 is the constant of variation

Inverse Variation- a function that can be written in the form xy = k or y = k/x. The product of the quantities remains constant, so as one quantity increases, the other decreases

the length x and the width y of a rectangle with a fixed area vary inversely. If the area is 40, xy = 40

Constant of Variation for Inverse Variation- the nonzero constant k in the function y = k/x

for the equation y = 8/x, 8 is the constant of variation

Inductive Reasoning- making conclusions based on observed patterns

Conjecture- conclusions reached by inductive reasoning

Sequence- a number pattern

-4, 5, 14, 23

Term- a number, variable, or the product or quotient of a number and one or more variables

the expression 5x + y/2 - 8 has three terms: 5x, y/2, and -8

Arithmetic Sequence- a number sequence formed by adding a fixed number to each previous term

4, 7, 10, 13, . . .

Common Difference- the fixed number added to each term of an arithmetic sequence

the common difference is 3 in the arithmetic sequence 4, 7, 10, 13, . . .

Properties and Formulas

Arithmetic Sequence

The form for the rule of an arithemetic sequence is A(n) = a + (n - 1)d, where A(n) is the nth term, a is the first term, n-1 is the term number, and d is the common difference

Find the tenth term of the sequence that has the rule A(n) = 32 + (n - 1)(-2)

A(10) = 32 + (10 - 1)(-2)

Direct Variation

y = kx or k = y/x

5x + 2y = 0 --> y = -5/2x

Inverse Variation

General Form of Inverse Variation

k = xy or y = k/x

5(7) = k --> xy = 35

Finding the Missing Coordinate

x1(y1) = x2(y2)

(3,8), (2,y) --> 3(8) = 2(y2)

*Vertical-Line Test (graph below)

A line would pass through (3,0) and (3,2), so the relation is not a function

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CHAPTER 6

Vocabulary

Rate of Change- the relationship between two quantities that are changing. The rate of change is also called slope

change in the dependent variable/change in the independent variable

Slope- the ratio of the vertical change to the horizantal change

*

Linear Function- a functions that graphs a straight line

y = -1/2x + 1

Linear Parent Function- the simplest form of a linear function

y = x

Linear Equation- an equation that models a linear function

y = 2x

y-intercept - the y-coordinate of the point where a line crosses the y-axis

y-intercept of y = 5x + 2 --> 2

Slope-Intercept Form- a linear equation of a nonvertical line written as y = mx + b, where m is the slope and b is the y-intercepty = 8x + 2

Standard Form of a Linear Equation- the form of a linear equation Ax + Bx = C, where A, B, and C are real nubers and A and B are both not 0

6x - y = 12

x-intercept- the x-coordinate of the point where a line crosses the x-axis

x-intercept of 3x + 4y = 12 --> 3

Point-Slope Form- a linear equation of a nonvertical line written as y - y1 = m(x - x1). The line passes through the point (x1,y1) with the slope mm = -1/2; passes through (2,-1) --> y + 1 = -1/2(x - 2)

Parallel Lines- two lines in the same plane that never intersect. Parallel lines have the same slope

**

Perpendicular Lines- lines that intersect to form right angles. Two line are perpendicular if the product of their slopes is -1

***

Negative Reciprocal- a number of the form -b/a, where a/b is a nonzero rational number. The product of a nuber and its negative reciprocal is -1

2/5 --> -5/2; (2/5)(-5/2) = -1

Line of Best Fit- the most accurate trend line on a scatter plot showing the relationship between two sets of data

****

Absolute Value Equation- equation whoes graph forms a V that opens up or down

*****

Translation- a translation that shifts a graphh horizontally, vertically or both

******

Properties and Formulas

Slope

Slope

vertical change/horizantal change = rise/run = change in the dependent variable/change in the independent variable = y2 - y1/x2 - x1 (where x2 - x1 ≠ 0)

*

Slopes of Horizantal Lines

The slope of horizantal lines is 0

(4,2) = (x2,y2), (1,2) = (x1,y1) --> 2-2/4-1 --> 0/3 = 0

Slopes of Vertical Lines

Division by 0 is undefined, so the slope of vertical lines is undefined

(4,2) = (x2,y2), (4,-1) = (x1,y1) --> 2 - (-1)/ 4 - 4 --> 3/0

Slopes of Parallel Lines

Nonvertical lines are parallel if they have the same slope and different y-intercepts. Any two vertical lines are parallel

**

Slopes of Perpendicular Lines

Two lines are perpendicular if the product of their slopes is -1. A vertical and a horizantal line are perpendicular

***

Slope-Intercept Form of a Linear Equation

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept

y = -2/3x + 5/3

Point-Slope Form of a Linear Equation

The point-slope form of the equation of a non vertical line that passes through the point (x1, y1) with slope m is y - y1 = m(x - x1)

y - 1 = -2/3(x - 1)

Standard Form of a Linear Equation

The standard form of a linear equation is Ax + By = C, where A, B, and C are real numbers and A and B are not both zero

2x + 3y = 5

*Slope (graph below)

the slope of the line below is 2/4 = 1/2

**Parallel Lines (graph below)

lines l and m are parallel

***Perpendicular Lines (graph below)

lines l and m are perpendicular

****Line of Best Fit (graph below)

*****Absolute Value Equation (graph below)

y = |3 - x|

******Translation

y = |x + 2| is a translation of y = |x|

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CHAPTER 7

Vocabulary

System of Linear Equations-

Solution of a System of Linear Equations-

No Solution-

Infinitely Many Solutions-

Substitution Method-

Elimination Method-

Linear Inequality-

Solutions of an Inequality-

System of Linear Inequalities-

Solution of a System of Linear Inequalities-

Properties and Formulas

Solutions of Systems of Linear Equations

A system of linear equations can have one solution, no solution, or infinitely many solutions

If the lines have different slopes, the lines intersect, so there is one solution.

If the lines have the same slopes and different y-intercepts, the lines are parallel, so there are no solutions.

If the lines had the same slopes and the same y-intercept, the lines are the same, so there are infinitely many solutions.

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CHAPTER 8

Vocabulary

Scientific Notation-

Geometric Sequence-

Common Ratio-

Exponential Function-

Exponential Growth-

Growth Factor-

Compound Interest-

Interest Period-

Exponential Decay-

Decay Factor-

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CHAPTER 9

Vocabulary

Monomial-

Degree of a Monomial-

Polynomial-

Standard Form of a Polynomial-

Degree of a Polynomial-

Binomial-

Trinomial-

Difference of Squares-

Perfect-Square Trinomial-

Factor by Grouping-

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CHAPTER 10

Vocabulary

Quadratic Function-

Standard Form of a Quadratic Function-

Quadratic Parent Function-

Parabola-

Axis of Symmetry-

Vertex-

Minimum-

Maximum-

Quadratic Equation-

Standard Form of a Quadratic Equation-

Roots of the Equation-

Zeros of the Function-

Zero-Product Property-

Completeing the Square-

Quadratic Formula-

Discriminant-

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CHAPTER 11

Vocabulary

Radical Expression-

Rationalize-

Like Radicals-

Unlike Radicals-

Conjugates-

Radical Equation-

Extraneous Solution-

Square Root Function-

Trigonmetric Ratios-

Sine-

Cosine-

Tangent-