f(x) = x 3x - 6 (a) Find the domain of f. (b) Identify any vertical asymptotes of the graph of y =...

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f(x) = x 3x - 6 (a) Find the domain of f. (b) Identify any vertical asymptotes of the graph of y = f(x). (c) Identify any holes in the graph. (d) Find the horizontal asymptote, if it exists. (e) Graph the function using a graphing utility and describe the behavior near the asymptotes
	
Document Preview: VCU Math 151|Worksheet 4.1
Name:
x
1. f(x) =
3x 6
(a) Find the domain of f.
(b) Identify any vertical asymptotes of the graph of y = f(x).
(c) Identify any holes in the graph.
(d) Find the horizontal asymptote, if it exists.
(e) Graphthefunctionusingagraphingutilityanddescribethebehaviorneartheasymptotes.2
x  x 12
2. f(x) =
2
x +x 6
(a) Find the domain of f.
(b) Identify any vertical asymptotes of the graph of y = f(x).
(c) Identify any holes in the graph.
(d) Find the horizontal asymptote, if it exists.
(e) Graphthefunctionusingagraphingutilityanddescribethebehaviorneartheasymptotes.

Robert · Accepted Answer

1. Use the six step procedure to sketch the graph of f(x) = 
2
1
310
xx
+-
(a) Find the domain.
2
3100(as denominator can not be zero)
(2)(5)0
2,5
{5,2};(,5)(5,2)(2,)
domain
xx
xx
x
domainxRorx
=
+-¹
-+¹
¹-
=Î--Î-¥-È-È¥
(b) Factor and reduce, if possible.
poles are -5 and 2.
Hence factors of 
2
310(2)(5)
xxxx
+-=-+
2
11
310(2)(5)
xxxx
=
+--+
(c) Find any x- and y- intercepts.
Put x=0
1
()
10
fx
=-
(y-intercept)
But 
()0
fx
¹
for any x , hence no x intercept
(d) Find any vertical asymptotes, and holes.
Only points to consider are x=-5,2 , zeros of denominator. As numerator does not contain any variable term , hence both points will serve as vertical asymptote and there is no holes.
Vertical asymptotes :- x=-5 and x=2
As x approaches -5- , f(x) approaches +∞
As x approaches -5+ , f(x) approaches -∞
As x approaches 2- ,

f(x) = x 3x - 6 (a) Find the domain of f. (b) Identify any vertical asymptotes of the graph of y = f(x). (c) Identify any holes in the graph. (d) Find the horizontal asymptote, if it exists. (e) Graph...

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