Download Graphing Rational Expressions Name: (a.) Given: x2 – 9. Set the

Graphing Rational Expressions
Name:
(a.) Given: x2 – 9. Set the expression equal to zero and solve for x:
x=
(b.) Given: x2 + 6x + 8. Set the expression equal to zero and solve for x:
x=
(c.) Given: x – 1. Set the expression equal to zero and solve for x:
x=
On the computer: Graph part (c) divided by part (a). What did you type? y =
Answer the following questions about the graph. Circle which piece each aspect comes from.
x-intercept(s)/Zero (write as an ordered pair)
vertical asymptote(s)
Domain:
Horizontal asymptote:
Numerator/Denominator (circle one)
(not just a number!) Numerator/Denominator (circle one)
Numerator/Denominator (circle one)
. Circle the correct acronym: BOBO
Type in your vertical and horizontal asymptotes to make sure you got them right.
Copy the graph from your computer screen.
BOTN
ESC
ERASE! Now graph part (b) divided by part (a). What did you type in? y =
Answer the following questions about the graph. Circle which piece each aspect comes from.
x-intercept(s)/Zero (write as an ordered pair)
vertical asymptote(s)
(not just a number!) Numerator/Denominator (circle one)
Domain:
Horizontal asymptote:
Numerator/Denominator (circle one)
Numerator/Denominator (circle one)
. Circle the correct acronym: BOBO
BOTN
ESC
Range:
Copy the graph from your computer screen.
ERASE! Now graph part (a) divided by part (c). What did you type in? y =
Answer the following questions about the graph. Circle which piece each aspect comes from.
x-intercept(s)/Zero (write as an ordered pair)
vertical asymptote(s)
(not just a number!) Numerator/Denominator (circle one)
Domain:
Horizontal asymptote:
Numerator/Denominator (circle one)
Numerator/Denominator (circle one)
. Circle the correct acronym: BOBO
Range:
Copy the graph from your computer screen.
BOTN
ESC
Vertical Asymptotes:
To find vertical asymptotes, you
Find the vertical asymptotes of these functions. Write them as equations!!
1.
2x 1
f ( x) 
4x  3
3.
f ( x) 
5.
7.
2.
x2
f ( x) 
x2
x2  7 x
x3
4.
f ( x) 
5x  7
10 x  3
f ( x) 
2x
x 9
6.
f ( x) 
2x
x x
f ( x) 
x2  5
x 2  9 x  20
8.
f ( x) 
7
x9
2
2
.
Horizontal Asymptotes:
To find horizontal asymptotes, you can use the following acronyms:
Identify the degree of the numerator and denominator and compare.
BOBO (Bigger on Bottom Zero
BOTN (Bigger on Top None)
ESC(Exponent Same Coefficients)
Identify the acronym and write the equation of the horizontal asymptote if one exists, otherwise write none,
1.
f ( x) 
2x 1
4x  3
2.
x2
f ( x) 
x2
Acronym:
Acronym:
Equation:
Equation:
3.
f ( x) 
x2  7 x
x3
4.
f (x) 
Acronym:
Acronym:
Equation:
Equation:
5.
f ( x) 
x2  4
x5
6.
f ( x) 
Acronym:
Acronym:
Equation:
Equation:
7.
f ( x) 
2x2  x 1
4 x2  1
8.
f ( x) 
Acronym:
Acronym:
Equation:
Equation:
3x
x3
1
x2
x 3
x2  9