Pre-Calculus Unit 2 Lesson 1
Pre-calculus (H)
Book Reference 1.2
Unit 2 Lesson 1: Finding the domain and range of a function
Objective: ______________________________________________________________
1. Do Now: Find the domain and range of the following function f(x) shown in
the graph. Use interval notation to describe the domain and range.
Domain:
Range:
2. Guided Practice: The Analytical Rules of Domain
Rule #1 Polynomial Functions and Odd Root
Rules #2 Square Root Functions:
2
Functions: f ( x)  x  1
g ( x)  x  3  2
1. Find the domain of f(x) algebraically.
1. Find the domain of g(x) algebraically.
2. Write the rule in your own words.
2. Write the rule in your own words.
_______________________________________________ _______________________________________________
_______________________________________________ _______________________________________________
3. Create your own example of this type of
3. Create your own example of this type of
function and find the domain using interval
function and find the domain using interval
notation.
notation.
Rule #3 Rational Functions
x -1
h(x) = 2
x - 4x - 5
1. Find the domain of h(x) algebraically.
Rule #4 Square Root in the Denominator
3
f ( x) 
x4
1. Find the domain of f(x) algebraically.
2. Write the rule in your own words.
2. Write the rule in your own words.
_______________________________________________ _______________________________________________
_______________________________________________ _______________________________________________
3. Create your own example of this type of
3. Create your own example of this type of
function and find the domain using interval
function and find the domain using interval
notation.
notation.
Pre-Calculus Unit 2 Lesson 1
3. Group Practice: Representing Domain and Range Algebraically, Numerically,
Graphically, and Analytically
Algebraic Representation
Graphical Representation
Directions: Find the following domain of
Directions: Graph the function on the graphing
the function algebraically.
calculator to check if your domain matches the
domain you got in the algebraic section. Sketch the
x3
f ( x) 
graph below.
2 x
Analytical
Directions: Answer the following questions.
1. What is the domain of the function in interval
notation?
2. What is the range of the function in interval
notation?
Key Notes/Reminders
Pre-Calculus Unit 2 Lesson 1
Unit 2 Lesson 1
Pre-Calculus (H) Homework: Complete the following handout.
For questions 1-8, find the domain of each function algebraically and the range of each
function graphically. Write the domain and range of the function in interval notation. Do
all work on a separate sheet of paper so you can make corrections if necessary.
1. f ( x) 
2 x
x  4 x  21
2
2. f ( x)  3 x  4
3. f ( x) 
1
2
x5
4. f ( x)  x  6  1
5. f ( x) 
16  x 2
x2
6. f ( x)   x 4  4
7. f ( x)   2 x  3
x2  x  2
8. f ( x)  2
x x2
9. Given the following graph of f(x), determine the domain and range of
the function using interval notation.