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 of
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*
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
No
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 = 9
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 n
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
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) Re
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 po
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°+ézx5xr
Math 138: Section 2.2
Polynomials of Higher Degree
Polynomials are smooth, continuous curves
' \§ 7 3
i) c.) 0 am" 6' a 3'
l 7 1/ Nu /
fl A! ,. . l {01) ~ jam/I r:
, ._ [CIA/.125
I u (IVA?)
F\/ i 1
/
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 +
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-
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 t