Section 1.5
Graphing Techniques: Transformations
MTH 175
We will use our knowledge of the shapes of these commonly used algebraic graphs and our understanding of
transformations to sketch transformed functions.
Vertical Shifts
Example #1: Given the graph

Section 1.3
MTH 175
Properties of Functions
Continuity: A function is continuous over an interval of its domain if its hand-drawn graph over that interval can
tinuous
drawn
be sketched without lifting the pencil from the paper.
8
7
6
5
4
3
2
1
determine t

Section 3.4
Properties of Rational Functions
MTH 175
A rational number is a ratio of integers. A rational function is a ratio of polynomials.
A rational function can be written in the form
p ( x)
R( x) =
where p ( x ) and q( x) are polynomials and q ( x)

Section 3.5
The Graph of a Rational Function
MTH 175
Calculus provides the tools required to graph a rational function accurately. In precalculus, we can gather quite a
bit of information about a rational graph to get an idea of the general shape and posi

Exam #1
MTH 175
Name_
Show all work and use proper mathematical notation to earn full credit.
Write your answers on the lines provided.
f ( x) 5 x2 2 x 4 , find
[6]
1. Let
[7]
2. Given
f ( x h) f ( x )
. Simplify your answer. _
h
f ( x) x2 and g ( x) 3 6

MTH 175
Collaborative Worksheet #1
Name_
Write your answers on the blanks provided.
Show all work to receive credit.
2
Collaborative Name _
f ( x + h) f ( x )
1a.
Let f ( x) = 3x 4 x 1 , find
b.
f ( x + h) f ( x)
. Simplify your answer.
Let f ( x) = 4 , f

Section 1.2
The Graph of a Function
MTH 175
Vertical Line Test
y is a function of x if a vertical line intersects the graph at only one point.
range,
,
Example #1: Determine the domain, range whether the relation is a function, intercepts, and x value giv

Section 1.4
Library of Functions; Piecewise-defined Functions
MTH 175
y
6
Lets review the graphs of commonly seen
functions. Knowing these graphs will lay the
foundation for further graphing techniques.
x
y=x
-5
-3
0
3
5
-5
-3
0
3
5
5
4
3
Sketch each of t

Section 1.1
Functions
MTH 175
Relation:
A relation is a correspondence between two sets.
Domain:
The domain of a function is the largest set of real numbers for which the function is defined._
n
Range:
The corresponding set of rea numbers that we obtain f