Worksheet 7: Absolute Value and PiecewiseDefined Functions
1. Given the following PiecewiseDefined Function
x2
f ( x ) x
2
, x 0
, 0 x 3
, x 3
a) Find the domain.
b) Sketch the function.
2. Given the following Absolute Value Functions
f ( x) 2 x 2 2 x
Worksheet 6: Other Algebraic Functions
1. For the functions
f ( x) 3 2 x 1
g ( x) 3 2 x 8 3
a) Find the domain of each function.
b) Graph the function using the method of transformations. Then state the range of the function.
c) Find the x and y intercept
Worksheet 5: Rational Functions
Useful algebraic properties and strategies pertaining to Rational Functions are expressed below.
Definition of a Rational Function
A rational function is a function that can be written in the form:
R( x)
p( x)
q ( x)
where
Worksheet 1: A Review of Functions and Relations
Match the graphs on the following pages with the algebraic equations of functions and
relations below. Write the letter identifying the graph next to the function or relation.
Polynomial Functions
f ( x ) 2
Worksheet 2: FACTORING ALGEBRAIC EXPRESSIONS
Factoring is the process of writing an algebraic expression as a product of two or more factors. In
the examples below, the techniques of finding factors with integer coefficients are illustrated. A
stepby ste
A Library of Basic Shapes
Even Power Function
eg. y x 2
Odd Power Function
eg. y x 3
Odd
Root
Function
eg. y 3 x
Absolute Value Function
eg. y x
Even Root Function
eg. y x
Rational Function
1
eg. y
x
Constant Function
eg. y 2
Identity Function
eg. y x
Ex
Worksheet 8: Finding the Derivative Function for Basic Shapes
For the following basic functions,
a) Graph the derivative function below each graph.
b) Use the limit definition of the derivative to find the algebraic form of the derivative function
and wri
1
Math 0131: Worksheet 9 Answers
A. Angle Measure
Angle:
220
Quadrant of terminal side:
III
50
IV
5
6
5
3
I
13
4

II
III
6
On +x axis
1.
2. Convert to degree measure:
3. Convert to radian measure:
9
12
195
radians = 135 degrees
=
13
12
4. A circle has
Worksheet 3: Quadratic Functions
A. Solving Quadratic Equations
The boxes below express some algebraic definitions, properties, and strategies that are useful when
solving quadratic equations in one variable.
COMPLEX NUMBERS
Definition of the Imaginary Un
Worksheet 4: Higher Degree Polynomial Functions
Useful algebraic properties and strategies pertaining to higher degree polynomial functions are
expressed below.
*Sketching Higher Degree Polynomial Functions:
A. Inspect the function to see if the method of