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 Dependent Variable

 Number of inequalities to solve: 23456789
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Precalculus Review

• Precalculus Review I
• Precalculus Review II
• The Cartesian Coordinate System
• Straight Lines

The Real Numbers

The real numbers can be ordered and
represented in order on a number line Inequalities, graphs, and notations

 Inequality Graph Interval   ) or ( means not included in the solution
] or [ means included in the solution

Intervals

 Interval Graph Example   Properties of Inequalities

 If a, b, and c are any real numbers, then Example Property 1 If a0,we have (-5)(2)<(-3)(2);that is ,-10< -6 Property 4 If abc -5<4,and -2<0,we have (-5)(-2)>(4)(-2);that is,10>-8

Absolute Value  Absolute Value Properties

 If a and b are any real numbers, then Example Property 5 l−a l= lal l−4l = −(−4) = 4 = l4l Property 6 la bl = lal lbl l(2)(−3)l = l−6l = l2l l−3l Property 7  Property 8  Exponents

 n,m positive integers Definition Example n factors  Laws of Exponents

 Law Example  Algebraic Expressions

• Polynomials
• Rational Expressions
• Other Algebraic Fractions

Polynomials Subtraction Polynomials

Multiplication Factoring Polynomials

•Greatest Common Factor • Grouping Factoring Polynomials

Difference of Two Squares: • Sum/Difference of Two Cubes: Factoring Polynomials

• Trinomials Roots of Polynomials

• Finding roots by factoring

(find where the polynomial = 0) Roots of Polynomials

• Finding roots by the Quadratic Formula

If ax2 + bx + c = 0 (a ≠ 0)

with a, b, and c real numbers,
then Example

Ex. Find the roots of 3x2 + 7x +1= 0 Rational Expressions

 Operation P, Q, R, and S are polynomials Addition Subtraction Multiplication Division

Rational Expressions Rational Expressions Other Algebraic Fractions

• Complex Fractions Other Algebraic Fractions

Notice: • Rationalizing a Denominator Cartesian Coordinate System Cartesian Coordinate System The Distance Formula The Distance Formula

Ex. Find the distance between (7, 5) and (-3, -2) The Equation of a Circle

A circle with center (h, k) and radius of

length r can be expressed in the form:

(x − h)2+ ( y − k )2= r2

 Ex. Find an equation of the circle with center at (4, 0) and radius of length 3 Straight Lines

• Slope
• Point-Slope Form
• Slope-Intercept Form

Slope – the slope of a non-vertical line
that passes through the points

(x1,y1)and (x2,y2)is given by: Ex. Find the slope of the line that passes through the points (4,0) and (6, -3) Slope

Two lines are parallel if and only if their
slopes are equal or both undefined

Two lines are perpendicular if and only if
the product of their slopes is –1. That is,
one slope is the negative reciprocal of the
other slope (ex. 3/4 a n d -3/4 ).

Point-Slope Form

An equation of a line that passes through
the point with slope m is given

by:
y − y1 = m x − x1

Ex. Find an equation of the line that passes through (3,1)
and has slope m = 4. Slope-Intercept Form

An equation of a line with slope m and
y-intercept ( 0 , b ) is given by:

y = mx + b Vertical Lines Horizontal Lines Example

Find an equation of the line that passes
through (-2, 1) and is perpendicular to the line
y = 2x − 7.

Solution:

Step 1.Since the slope of the line y=2x - 7 is 2,

we have the slope of the perpendicular line is m=-1/2 .

Step 2. Example

Find an equation of the line that passes through
(0, 1) and is parallel to the line 6x + 2 y = 5.

Solution:

Step 1.We need to find the slope of the line

6x + 2 y = 5. The slope of the parallel line is also m=-3.

Step 2.
Since m=-3 and b=1, 