MA 105 Rational Functions and Conic Sections - In exercises...

In exercises 1 and 6, determine the domain and intercepts of the given function.
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=

X-INTERCEPT: Plugging f(x) =0, we get x=
2
3

as X-intercept, hence X-intercept is (
2
3

, 0)
Y-INTERCEPT: Plugging x=0 we do not get any Y-intercept as function is not defined at y=0
In exercises 14, 16, and 18 determine the vertical and horizontal asymptotes of the graph of the
given function. Sketch the graph. Then, determine appropriate WINDOW values, and check your
answer using your graphing calculator. Choose the viewing rectangle carefully to obtain a correct
and complete representation of the function. Be sure that your viewing rectangle is large enough to
indicate the asymptotic behavior of the function. You may not always be able to show all of the
important behavior of the function in one viewing rectangle.
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Graph:

16.
f
(
x
)
=
x
2
+ 1
x
2
+ 2 x − 3
Vertical Asymptote:
2
2 3 0
( 1)( 3) 0
1
3
x x
x x
x
x
  
  

 
Horizontal Asymptote:
f
(
x
)
=
x
2
x
2
= 1
y = 1
Graph:

18.
f ( x ) =
x 2 − 1
x + 2
Vertical Asymptote:
2 0
2
x
x
 
 
Slant Asymptote:
f ( x ) = ( x − 2 ) +
3
x + 2
y = x − 2

Graph:
In exercises 22 and 26, determine the domain and sketch the graph of the reducible function.