Pre-Calculus
Name:______________________
Unit 1: Functions Day 2
Date:_________________
Today’s Objective: Students will review basic characteristics of a function.
Function Definition: A relation (set of points) in which each x-value is assigned to only one y-value….it
passes the vertical line test.
One-to-One relation: A relation (set of points) in which each y-value is assigned to only one x-value….it
passes the horizontal line test.
X-intercept: Point on the graph where the
relation touches the x-axis (y = 0). Goes
by root, zero, or solution.
Y-intercept: Point on the graph where the
relation touches the y-axis (x = 0).
Interval Notation: Intervals can be shown using inequalities or with parenthesis (not equal) and square
brackets (equal).
Example 1: -∞ < x ≤ 5
Example 2: 7 ≤ x < 19
Increasing: A relation increases on an interval
if as x increases, y increases (notation is domain
value).
Decreasing: A relation decreases on an interval
if as x increases, y decreases (notation is domain
value).
Constant: A relation is constant over an interval
if it remains at the same value (notation is domain
value).
Answer the following questions using the graph below.
www.bluepelicanmath.com
The following notation is used for operations on and the composition of functions:
In the following examples, assume that 𝑓(𝑥) = 𝑥 2 − 4𝑥 + 1 and 𝑔(𝑥) = 3𝑥 − 2 and perform the
indicated operation.
1. (𝑓 + 𝑔)(𝑥)
𝑓
4. (𝑔) (𝑥)
2. (𝑓 − 𝑔)(𝑥)
5. (𝑓 ◦ 𝑔)(𝑥)
Functions can be classified into the categories of even, odd, or neither.
3. (𝑓𝑔)(𝑥)
In the following examples, determine if the graph is even, odd, or neither:
7. Complete the table to determine if 𝑓(𝑥) = 𝑥 2 + 1 is even, odd or neither. The domain is restricted to
{ 1, 2, 3, -1, -2 }.
Practice:
Name ________________________
Domain & Range:
State the domain and range and determine if each relation is a function.
 5 

1)  , 2  ,  3,  1 ,  2.5,5  ,  4,5  
 2 

2)
10
5
4
7
y
3)
4)
x
5)
6)
-1
For question 7, use the following functions:
1
f ( x)  2 x 2  3x  1
g ( x)  x  4
2
k ( x)  5 x 2
h( x )  2 x  8
7) Find each of the following and state the domain.
a ) f ( x )  h( x )
c ) g ( x ) h( x )
b)

f ( x)
h( x )
d ) g ( x )  f ( x )  h( x )
Intercepts / Even-Odd Functions:
(1) State the domain and range of the function. (2) Determine if the function is even, odd or neither.
8. f(x) = 5x + 17
9. g ( x)  x  7
10. f(x) = –3x2 + 4
1
11. j ( x) 
x7
2
12. m( x) 
( x)( x  6)
13. f(x) = 2x3 – 4x