Download PRECALCULUS: Ch

Math Analysis HW – 3.3, 3.4
Graphing Rational Functions
1.] Graph f(x) =
Name _____________________
Date __________ Period _____
1
. Show all work and complete the following.
x 1
y
1)
Hole in graph:
2)
Vertical Asymptote:
3)
Horizontal Asymptote:
x
4)
x-intercept:
5)
y-intercept:
6)
Slant Asymptote:
7)
Points:
2.] Graph f(x) =
5 x  10
. Show all work and complete the following.
x x6
2
y
1)
Hole in graph:
2)
Vertical Asymptote:
3)
Horizontal Asymptote:
x
4)
x-intercept:
5)
y-intercept:
6)
Slant Asymptote:
7)
Points:
3.] Graph f(x) =
4x  3
. Show all work and complete the following.
x 1
y
1)
Hole in graph:
2)
Vertical Asymptote:
3)
Horizontal Asymptote:
4)
x-intercept:
5)
y-intercept:
6)
Slant Asymptote:
7)
Points:
4.] Graph f(x) =
x
4
. Show all work and complete the following.
x  6x  5
2
y
1)
Hole in graph:
2)
Vertical Asymptote:
3)
Horizontal Asymptote:
4)
x-intercept:
5)
y-intercept:
6)
Slant Asymptote:
7)
Points:
x
5.] Graph f(x) =
x 2  49
. Show all work and complete the following.
x2  8x  7
y
1)
Hole in graph:
2)
Vertical Asymptote:
3)
Horizontal Asymptote:
x
4)
x-intercept:
5)
y-intercept:
6)
Slant Asymptote:
7)
Points:
6.] Graph f(x) =
x2  5x  8
. Show all work and complete the following.
x3
1)
Hole in graph:
2)
Vertical Asymptote:
3)
Horizontal Asymptote:
4)
x-intercept:
5)
y-intercept:
6)
Slant Asymptote:
7)
Points:
y
x
7.] Graph f(x) =
 x 2  3x  10
. Show all work and complete the following.
x
y
1)
Slant Asymptote:
2)
Hole in graph:
3)
Vertical Asymptote:
4)
Horizontal Asymptote:
5)
x-intercept:
6)
y-intercept:
7)
Points:
8.] The cost of producing x units of a product is C = 0.2x2 + 10x + 5, and therefore the average
C
0.2 x 2  10 x  5
cost per unit is C =
=
, 0 < x.
x
x
Sketch the graph of the average cost function, and estimate the number of units that should be
produced to minimize the average cost per unit.
x
9.] Find the equation for the rational function shown below.
10.] Write a rational function satisfying the following criteria.
Vertical asymptote: x = -1
Slant asymptote: y = x + 2
Zero of the function: x = 3