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MATH 1148 Notes $10.49
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MATH 1148 Notes
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This folder contains comprehensive lecture notes for Math 1148, covering key topics in pre-calculus and introductory algebra. The materials provided offer in-depth explanations, examples, and problem-solving strategies. These lecture notes provide a solid foundation for mastering these essential ma...

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  • December 8, 2024
  • 1
  • 2024/2025
  • Class notes
  • Ander aguirre
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2 3 .




functions & relations con
Functions
S
Relations VS
from a set of values ists
I
from a set of values
any map any map
to another set of values
to another set of values
vehicle any "input"
has one "output"
person address person ~
owned in past social security citizen
person biological mother number
-




vertical line test
no point hits more than once !
-..
s hits x axise
if the vertical line hits more than once ,

the graph is not a function . function not a function


evaluating functions plug in number
replace every x with the function rule
&
f(x)
3
+ 2x in each
= =
3 plug
x
value for x ! solve expression
f (0) f(2) f(m + 2) , ,



↓ (0)
=




z +
2(0) = -




/3 f (z) =
2z 2(2)
+ =
3 + (m + z),my3 -
+ 2(m + 2)




another example A
: X" 3x
·

f(x) = -




f (a h) (a + h) - 3(a + h
2
f(x) X2-3X +
Suppose
= · = -



#
find & f(a+ h) -
f (a) =
(a + h)(a + h) 3(a +h) -




simplify
- h =
a2 + zah + h2 za 3h - -




* remember, the f is
a FUNCTION not a variable
f(a) al 3a
· = -




use one function ·f (a+h) +(a) a 2ahth2 3a-3h (a 3a)
=
- + -
-
-




1 =
h
at a time
h combinterms a
+ zahth-3a-3-a
h
:
2ah h3-sh
take each answer of the 2a + h
+


2
=
h
= -

3
into the
function to plug
next

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