Download 3.1 Do Now: functions

3.1 DO NOW: FUNCTIONS
• When is a relation a function?
ACADEMY ALGEBRA II/TRIG
3.1: FUNCTIONS
HW tonight: none
HW Monday: p.220 (24-32 even,
44,50,54,58,62,68,80)
QUIZ 3.1-3.2: NEXT THURS (9/26)
DETERMINE WHICH OF THE FOLLOWING
RELATIONS REPRESENTS A FUNCTION.
Education
GED
H.S. diploma
Some college
College grad
Unemployment
8.5 %
5%
4.2 %
2.7 %
Item
Burger
Sandwich
Salad
Fish
Height
IQ
66”
68”
70”
72”
110
120
130
140
Fat Calories
19
14
23
DETERMINE WHETHER EACH RELATION
IS A FUNCTION. IF IT IS STATE THE
DOMAIN AND RANGE.
a) (1,4), (2,5), (3,6), (4,7)
b) (1,4), (2,4), (3,5), (6,10)
c) (3,9), (2,4), (0,0), (1,1), (3,8)
DETERMINE IF THE EQUATION DEFINES
Y AS A FUNCTION OF X.
a) y  2 x  5
b) x 2  y 2  1
FIND THE VALUE OF A FUNCTION
The function y = f(x), has an independent
variable x, and a dependent variable y.
For the function y = f(x), defined by
2
f(x)= 2x – 3x, evaluate:
a) f(3)
b) f(x) + f(3)
c) 3f(x)
d) f(-x)
e) - f(x)
FIND THE VALUE OF A FUNCTION
For the function y = f(x), defined by
2
f(x)= 2x – 3x, evaluate:
f) f(3x)
g) f(x + 3)
h) (f(x + h) – f(x))/h
FINDING VALUES OF A FUNCTION ON
A CALCULATOR
Your calculator can evaluate the numerical
2
value of a function such as y = 2x – 3x in a
number of ways:
Insert the equation into y1, then use
a) y1(3) On the home screen type Y1(3) ENTER
b) Using tables Press TABLE (above F5) and
view values for the function.
THE DOMAIN OF A FUNCTION
• Often the domain of a function is not specified.
• In these cases, we agree that the domain of
the function, f, is the largest set of real numbers
for which the value f(x) is a real number.
• The domain of most functions are found by
excluding some values of x because they make
you divide by zero or take the even root of a
negative number.
FIND THE DOMAIN OF THE
FOLLOWING FUNCTIONS.
a) f ( x)  x  5x
2
x 1
b) g ( x)  2
x  5x  4
c) h( x)  x 2  4
FORM THE SUM, DIFFERENCE, PRODUCT,
AND QUOTIENT OF TWO FUNCTIONS.
 f  g x   f ( x)  g ( x)
 f  g x   f ( x)  g ( x)
 f  g x   f ( x)  g ( x)
f
f ( x)
 x  
g ( x)
g
• The domain of the
sum, difference, and
product consists of
the numbers x that
are in the domains of
both f and g.
• The domain of the quotient consist of the
numbers x for which g(x) does not equal zero
that are in the domains of both f and g.
FIND THE SUM, DIFFERENCE, PRODUCT,
AND QUOTIENT OF THE TWO FUNCTIONS.
DETERMINE EACH DOMAIN.
f ( x)  x 2  9, g ( x)  3x  5
f
 g  x  
f
 g  x  
 f  g x  
f 
  x  
g