The Graph of a Rational Function 4.3 - Math 121 Section 4.3...

Math 121 – Section 4.3 Solutions
7. R ( x ) =
x + 1
x ( x + 4)
• the domain is all x except x = 0 , - 4; there is no y -intercept
• the x -intercept is at x = - 1
• the vertical asymptotes are x = 0 and x = - 4
• the horizontal asymptote is y = 0
• table:
Interval ( -∞ , - 4) ( - 4 , - 1) ( - 1 , 0) (0 , ∞ )
Number Chosen - 5 - 2 -
1
2
1
Value of R R ( - 5) = -
4
5
R ( - 2) =
1
4
R ( -
1
2
) = -
2
7
R (1) =
2
5
Location of graph below x -axis above x -axis below x -axis above x -axis
Point on graph ( - 5 , -
4
5
) ( - 2 ,
1
4
) ( -
1
2
, -
2
7
) (1 ,
2
5
)
x
y
0
1
1
2
2
3
3
- 1
- 1
- 2
- 2
- 3
- 3 - 4 - 5 - 6 - 7
( - 5 , -
4
5
)
( - 2 ,
1
4
)
( - 1 , 0)
( -
1
2
, -
2
7
)
( - 1 ,
2
5
)
9. R ( x ) =
3 x + 3
2 x + 4
=
3( x + 1)
2( x + 2)
• the domain is all x except x = - 2; the y -intercept is at R (0) =
3
4
• the x -intercept is at x = - 1
• the vertical asymptote is x = - 2
• the horizontal asymptote is y =
3
2
1

• table:
Interval ( -∞ , - 2) ( - 2 , - 1) ( - 1 , ∞ )
Number Chosen - 3 -
3
2
0
Value of R R ( - 3) = 3 R ( -
3
2
) = -
3
2
R (0) =
3
4
Location of graph above x -axis below x -axis above x -axis
Point on graph ( - 3 , 3) ( -
3
2
, -
3
2
) (0 ,
3
4
)
x
y
0
1
1
2
2
3
4
5
- 1
- 1
- 2
- 2
- 3
- 3 - 4 - 5
( - 3 , 3)
( -
3
2
, -
3
2
)
( - 1 , 0)
(0 ,
3
4
)
12. R ( x ) =
6
x 2 - x - 6
=
6
( x - 3)( x + 2)
• the domain is all x except x = - 2 ,