Title of Lesson:
Introduction to Functions
Section: 1.2
Pages: 16-29
My Learning Goals
1. Functions – decide if a relation is a function. Use
function notation and evaluate functions. Use
functions to model applications
2. Find the Domain and Range of function and
represent them using interval notation.
3. Evaluate difference quotients.
Vocabulary/Formulas
1. Function – every input has one unique output.
2. Domain – The set of inputs for which the function is
defined.
3. Range – The set of possible outputs for a given function
4. Piece-wise function – A function that is defined by two or
more equation over a specific domain.
5. Difference Quotient-
f (x + h) - f (x)
,h ¹ 0
h
Prerequisite Skills with Practice
1. Evaluate the following
function for f(3), f(0)
and f(-3).
f (x) = -x + 3x - 3
2
2. Isolate “y” in the follow
equation.
(x -2) +(y+ 3) = 25
2
2
Notes
When is a relation a
function?
Tables:
Vertical Line Test.
Graphs:
Notes
Testing for functions
algebraically.
x + y =1
± sign.
x+ y =1
Looking for a
2
2
Notes
Piecewise-Defined
Function
Evaluating.
ì5 - 2x 2 , x < 0
Given f (x) = í
î2x + 5, x ³ 0
Evaluate f(-2), f(0), f(3)
Notes
Piecewise-Defined
Function
Sketching.
ì-2x +1,x < 2
f (x) = í
î x + 3,x ³ 2
ì x +1, x < -3
ï
g(x) = í2,-3 £ x £ 0
ï-x + 3, x > 0
î
Notes
Determining domains of
functions.
Need to consider the
values for which the
function is defined and
the real world implications
of the function.
f : {(-3,0),(-1,4),(0,2),(2,2),(4,-1)}
g(x)= -3x +4x+5
2
1
h(x) =
x+5
4
3
The volume of a sphere: V = p r 3
k(x) = 4 - 3x
Notes
The box problem.
Calculator Skills:
• Basic Input
• Adjusting Window
• Finding Maximums
A sheet of metal 12 inches by 10
inches is to be used to make a open
box. Squares of equal sides x are cut
out of each corner then the sides are
folded to make the box. Find the
value of x that makes the volume
maximum.
Notes
Difference Quotients
f (x + h)- f (x)
,h ¹ 0
h
Understanding graphically
and algebraically.
Find the Difference Quotient
for the functions below
and simplify your answer.
Homework
Assignment: Pg. 23
1, (5-9) odd (13-24) all (27-41) odd
(44-64) all 74,76,77, (87-90) all