Math 138: Section 1.9
Inverse Functions
Defn: A function f'1(x), read as "f inverse of x is called the inverse, off(x) ifand
only if (f°f1)(x) = x AND (flcfXx) = x
The domain off(x) is the gang ('2 off1(x), and the Yang f» of
f(x) is the LLDMQUB off1(x),i
Math 138: Section 1.5
Analyzing Graphs of Functions
Defn: The Q g oi ax R/ngar are the x-values where f(x)=O. (i.e., the
x-intercepts).
Ex: Find the zeros of the following functions:
3) f(x) = 3x 6
0* 3x4:
(023%
(lgxi
b) x) =x25x6
Xt- 95 O
(X 4:1 (15):0
X
Math 138: Section 1.4
Functions
5" i
Defn: A W, dwh f from a set A (x-values) to a set B (y-values) is a relation for
which every x has only one y.
Ex: Are the following relations functions?
v:
I
Nol m Funcm lflt. ; v (313 MAM M V
X; Z hid l6 "3?" ' m h
Math 138: Section 1.3
Linear Eguations in Two Variables
H II
Given y = mx + b, m is the slope and "b" is the y-intercept (where x = O)
The 61092. between two points (x1,y1) and (352,312) is: m = g = 93" : 1
rum AV X2_Xl
Slopes- WSHWLSRP" negaWopo erHLd
Math 138: Section 1.1
Rectangular Coordinates
Defn: The RHEth ulav CODY-[Lib QR Him or
Cw Lam
represented (Le. plotted).
Pyjhagorean Theorem:
PlLH m Pen/1J6
UWL Conchrlywo {lack Pod/Hs.
OHM
For (L nmt Jmangut
Z
az+b2fC
mm
b
Plan 5: : the 2-D plane such
Math 138: Section 1.2
Graphs of Eguations
Defn: E330 aims will TWO Vwi'ab :3; :The relationship between
two variables. g) Lg, {Uri
A: TTr" In is (ml-mix 3J1
{ : xl+ 1
Defn: A point is a éolu'hon to an equation if the statement holds true when you plug
t
Math 138: Section 1.6
A Library of Parent Functions
1) Constant Function: f(x) = c 2) Linear Function:f(x) = x
3) Quadratic Function (Parabola): f(x) = x2 4) Cubic Function:f(x) = x3
f lllxizx
5) Reciprocal Function: f(x) 2%
7) Absolute Value Function
Math 138: Section 1.7
Transformations of Functions
*Many functions have graphs that are simple transformations of the parent graph studied in
section 1.6.
Vertical and Horizontal Shifts:
Let c be a positive real number. for-Hm and HDYI ZOYih/i shifts in t
Math 138: Section 2.3
Poiynomial and Synthetic Division
I We can use poiynomial long division to factor.
Example: Factor 2614+ 5x3 + 6x2 x 2 by using long division to divide byx + 2
5i2 3; +§x°+ézx5xra
353+GXL )(f-erngxtX-él '7 (W17ohgx fl)
H 313242)?)
Lx
Math 138: Section 2.1
Quadratic Functions
Defn: Let n be a non-negative integer and let an, an_1, , a2, £11,110 be real numbers with
an at 0. Then the function given by f(x) = anxl + anxn1 + + azxz + alxl + a0 is the
polynomial function ofdegree n.
Note
Math 138: Section 1.8:
Combinations of Functions: The Composition Function
We can perform the four basic operations between two functions: (Kl . 13%)
Addition: «P r (x7: J; (K) lr 30)
Subtraction: (4-3004) : «COO 3650
Multiplication:
Division: f
( '
Ex
Math 138: Precalculus
Practice Test 1
Name:_
1) Given the points (-2,6) and (4,-6) find
a. the midpoint of the line segment joining the points
b. the distance between the points
c. find the slope of the line between the points
d. find the equation of the