While working on these below on your own paper, have last night's assignment out on your desk!
Completely factor each of the following:
1.4 Functions
Def: A relation is a set of pairs of #s that are related to
one another by some rule.
Def : A Function is a relation in which each value from the
1st set is matched to exactly one value from the 2nd set
Radius
1
4
Area of circle
16 π
3
π
2
4π
9 π
Aug 17­10:40 AM
4 ways to represent a function:
1.
Verbally -- describe the relationship
2.
Numerically -- list of ordered pairs or an x/y
table
3.
Graphically --input on x-axis, output on yaxis
4. Algebraically --equation
EX: Function?
A. X is the # of state
representatives and y
is the # of senators
from that state
x
2
2
3
3
4
y
11
10
8
5
2
Determine if each of the following is a function.
ex 1)
ex 2)
B.
y
4
C.
2
x
0
­4
­3
­2
0
­1
1
2
3
4
­2
­4
Aug 19­12:38 PM
1
If an equation represents a function, you may use
function notation to represent it. ( i.e: f(x) = x 2 )
Find each of the following:
EX: If f(x) = - x2 + 4x + 1, find each:
a. f(2)
b. f(t)
c. f(x + 2)
ex 1) f(-3)
ex 2) f(0)
ex 3) f(2)
Aug 19­12:40 PM
Have HWK out and TRY THESE!
Day 1 Assignment:
Read: Section 1.4
Do: p. 48 #1 –19 odd, 29, 35, 37
1. Give a graphic example of a relation that is a function.
2. Give a numeric example of a relation that is not a function.
3. Give an algebraic example of a relation.
4. If f(x) = ­2x2 ­ 7x, find f(x ­ 3).
5. If g(x) = ­3x3, x < ­2
­x ­ 5, w > ­2
Find g(­3), g(­2), g(­1)
Aug 19­7:47 AM
2
DEF: The domain of a function is the set of
all input values that DO NOT cause:
Name the domain of each function
using interval notation where
appropriate.
A. {( -3, 0), (-1, 4), (0, 2), (2, 2), (4, -1)}
•division by zero
•even root of a negative
B. F(x) = -3x 2 + 4x + 5
C. G(x) = 1/(x + 5)
DEF: The range of a function is the set of
all output values that resulted from the
input values
A basic calculus formula used to approxmate the slope of a tangent line to a curve!
D. V = 4/3 πr 3
E. K(x) =
4 −3 x
EX: For g(x) = x 2 - 4x + 7, find the difference quotient
of g(x).
f ( x + h ) − f ( x)
h
Ex: For f(x) = -2x +4, find the difference quotient.
3
Assignment:
Read: Section 1.5
Do: p. 50 #43 –69 odd, 79 –85 odd
Aug 17­10:39 AM
4