3.1 DO NOW: FUNCTIONS

•When is a relation a function?

QUIZ 3.1-3.2: NEXT THURS (9/26)

ACADEMY ALGEBRA II/TRIG3.1: FUNCTIONS

HW tonight: noneHW Monday: p.220 (24-32

even, 44,50,54,58,62,68,80)

DETERMINE WHICH OF THE FOLLOWING RELATIONS REPRESENTS A FUNCTION.

Education Unemployment Height IQGED 8.5 % 66” 110H.S. diploma 5 % 68” 120Some college 4.2 % 70” 130College grad 2.7 % 72” 140

Item Fat CaloriesBurger 19Sandwich 14Salad 23Fish

DETERMINE WHETHER EACH RELATION IS A FUNCTION. IF IT IS STATE THE

DOMAIN AND RANGE.a)

b)

c)

)7,4(),6,3(),5,2(),4,1(

)10,6(),5,3(),4,2(),4,1(

)8,3(),1,1(),0,0(),4,2(),9,3(

DETERMINE IF THE EQUATION DEFINES Y AS A FUNCTION OF X.

a)

b)

52 xy

122 yx

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

f(x)= 2x2 – 3x, evaluate: a) f(3) b) f(x) + f(3) c) 3 f(x) d) f(-x) e) - f(x)

FIND THE VALUE OF A FUNCTION

For the function y = f(x), defined by

f(x)= 2x2 – 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 value of a function such as y = 2x2 – 3x in a number of ways:Insert the equation into y

1, then use

a) y1(3)

b) Using tables

On the home screen type Y1(3) ENTER

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)

b)

c)

xxxf 5)( 2

45

1)(

2

xx

xxg

4)( 2 xxh

FORM THE SUM, DIFFERENCE, PRODUCT, AND QUOTIENT OF TWO

FUNCTIONS.

)(

)(

)()(

)()(

)()(

xg

xfx

g

f

xgxfxgf

xgxfxgf

xgxfxgf

• 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.53)(,9)( 2 xxgxxf

xg

f

xgf

xgf

xgf