3.1 do now: functions when is a relation a function?
TRANSCRIPT
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