College Algebra Quick Reference Sheet printable pdf download

College Algebra Quick Reference Sheet

Function Notation y = f(x)

Lines or Linear Functions

Parabolas or Quadratic Functions

Domain

Set of all valid x

Slope of Line through points (x

, y

) & (x

, y

)

Range

Set of all valid y

Set Notation

General Form

Interval Notation

Set-Builder Notation

The graph has a smile if a is positive and a frown

Function Arithmetic

(a, b)

{ x | a < x < b }

if a is negative, and has a vertex at coordinates:

Slope-Intercept Form - slope m and point (0, b)

{ x | a ≤ x ≤ b }

[a, b]

{ x | a ≤ x < b }

[a, b)

Point-Slope Form - slope m and point (x

, y

)

{ x | a < x ≤ b }

(a, b]

Vertex Form

(a, ∞)

{ x | a < x }

[a, ∞)

{ x | a ≤ x }

The graph has a smile if a is positive and a frown

(-∞, b)

{ x | x < b }

Horizontal Line through point (0, b)

if a is negative, and has a vertex at (h, k).

{ x | x ≤ b }

(-∞, b]

Transformations of Graphs of Functions

Vertical Line through point (a, 0)

Special Factoring Formulas

Set Operations

Horizontal

Vertical

Operation

Elements

Logic

Shift

(left)

(up)

Average Rate of Change

(right)

(down)

Union

All

Reflect

(y-axis)

(x-axis)

Intersection

Common

AND

The average rate of change m for function y=f(x)

between x=a and x=b is

Scale

(compress)

(expand)

1. Subtract h from each of the x-coordinates of

Coordinate Plane Quadrants

the points on the graph of f. This results in a

horizontal shift to the left if h > 0 (positive h) or

right if h < 0 (negative h).

III

Absolute Value Properties

2. Divide the x-coordinates of the points on the

Special Product Formulas

graph obtained in Step 1 by b. This results in a

horizontal scaling, but may also include a

Distance and Midpoint Formulas

reflection about the y-axis if b < 0 (negative b).

If P

=(x

) and P

=(x

) are two points,

3. Multiply the y-coordinates of the points on

the distance between them is

the graph obtained in Step 2 by a. This results in

a vertical scaling, but may also include a

reflection about the x-axis if a < 0 (negative a).

and the midpoint coordinates are

Absolute Value Function as a

4. Add k to each of the y-coordinates of the

Piecewise-Defined Function

points on the graph obtained in Step 3. This

results in a vertical shift up if k > 0 (positive k)

Quadratic Formula

or down if k < 0 (negative k).

Solve

Intercepts of an Equation

x-intercepts

Set y = 0; solve for x

Properties of Equality

Absolute Value Equations and Inequalities

y-intercepts

Set x = 0; solve for y

If c is a positive number:

, then 2 real unequal solutions

Symmetry of the Graph of an Equation

, then 2 real duplicate solutions

Type

Mathematical

Geometrical

Unchanged when

, then no real solutions

Unchanged when

x-axis

reflected about

Properties of Inequalities

y replaced by -y

x-axis

Factored Form for real factors:

Unchanged when

y-axis

reflected about

x replaced by -x

y-axis

Unchanged when

y replaced by –y &

origin

rotated 180°

Page 1

x replaced by -x

about origin

College Algebra Quick Reference Sheet

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