menu
Qammunity.org
Login
Register
My account
Edit my Profile
Private messages
My favorites
Ask a Question
Questions
Unanswered
Tags
Categories
Ask a Question
Determine the holes, vertical asymptotes and horizontal asymptotes of the rational function <img src="-f-y-3D3x-5E2-2B10x-8-2Fx-5E2-2B7x-2B12-3Cbr-20-2F-3E.jpg"> Could you also show your work because I need to know how to do this for an upcoming test. Thanks in advance.
asked
Jan 23, 2019
167k
views
2
votes
Determine the holes, vertical asymptotes and horizontal asymptotes of the
rational function
Could you also show your work because I need to know how to do this for an upcoming test. Thanks in advance.
Mathematics
high-school
Ken Lin
asked
by
Ken Lin
8.3k
points
answer
comment
share this
share
0 Comments
Please
log in
or
register
to add a comment.
Please
log in
or
register
to answer this question.
1
Answer
3
votes
I could give you some answers and then depend on you to ask questions until you're satisfied that you know enough to take your upcoming test.
horiz. asymp.: Focus on the dominant (highest x power) terms of the numerator and denominator. They are 3x^2 and x^2 repsectively. Dividing 3x^2 by x^2, we get 3. The horiz. asympt. is merely y=3. It's not always this easy, tho'.
vert. asymptote depends upon the denominator alone. You must find the roots of the denom.: x^2 + 7x + 12. They are -3 and -4. Notice how x^2 + 7x + 12 = (x+3)(x+4). The vertical asymptotes are x=-3 and x=-4.
Now just suppose that the numerator and denominator of your function share a common factor (which means you can cancel out that factor). But we're not off the hook yet! Suppose that the factor common to numerator and denominator is (x+3). You can cancel this out, removing it from both numerator and denominator, but when you graph the rational function, you must place a circle at the root showing that x cannot have that particular value. If, as I supposed, (x+3) is a common factor, then leave a circle at x=-3 on your graph. "Holes" show up in straight lines. For more info on holes I urge you to do an int. search for "holes in rational function graphs" ... I found a great explanation that way.
Nicholaswmin
answered
Jan 27, 2019
by
Nicholaswmin
8.4k
points
ask related question
comment
share this
0 Comments
Please
log in
or
register
to add a comment.
← Prev Question
Next Question →
Related questions
asked
Dec 26, 2018
188k
views
Find the quotient of the quantity [tex] \frac{4x^3y+12x^2y^3-20xy}{4xy} [/tex]. A.<img src="-f--3Cbr-20-2F-3E-20x-5E2-2B3xy-5E2-2B5.jpg"> B. <img src="-f--3Cbr-20-2F-3E-20x-5E2-2B3xy-5.jpg"> C. <img src="-f--3Cbr-20-2F-3E-204x-5E3y-2B12x-5E2y-5E3-5.jpg"> D. <img src="-f--3Cbr-20-2F-3E-20x-5E2-2B3xy-5E2-5.jpg"> Please tell me how to get the correct answer! Thank you!
Rhlsthrm
asked
Dec 26, 2018
by
Rhlsthrm
7.9k
points
Mathematics
middle-school
2
answers
4
votes
188k
views
asked
Nov 25, 2018
76.0k
views
This is a question on my partial fractions homework, but no matter what I try I can't figure it out.. <img src="-f--5Cint-5Climits-5E2_0-20-7B-5Cfrac-7B(x-5E2-2Bx-2B1)-7D-7B(x-2B1)-5E2(x-2B2)-7D-20-7D-20-5C-2C-20dx-20-3Cbr-20-2F-3E-3Cbr-20-2F-3E.jpg">
Ncakmak
asked
Nov 25, 2018
by
Ncakmak
8.2k
points
Mathematics
college
1
answer
2
votes
76.0k
views
asked
Jul 9, 2021
146k
views
Which inequality represents all values of x for which the quotient below is defined? <img src="-f--5Csqrt-7B7x-5E2-20divided-20by-20-5Csqrt-7B3x-7D-3Cbr-20-2F-3E-3Cbr-20-2F-3E-3Cbr-20-2F-3E-3Cbr-20-2F-3E-20-5C-5CA.-20x-20-5C-20-5Ctextgreater-20-5C-201-20-5C-5CB.-20x-20-5C-20-5Ctextgreater-20-5C-20-1-5C-5CC.-20x-20-5C-20-5Ctextgreater-20-5C-200-5C-5CD.-20x-20-5Cgeq-200.jpg">
Tushar Mate
asked
Jul 9, 2021
by
Tushar Mate
8.2k
points
Mathematics
high-school
1
answer
4
votes
146k
views
Ask a Question
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.
9.4m
questions
12.2m
answers
Other Questions
How do you can you solve this problem 37 + y = 87; y =
What is .725 as a fraction
How do you estimate of 4 5/8 X 1/3
A bathtub is being filled with water. After 3 minutes 4/5 of the tub is full. Assuming the rate is constant, how much longer will it take to fill the tub?
i have a field 60m long and 110 wide going to be paved i ordered 660000000cm cubed of cement how thick must the cement be to cover field
Twitter
WhatsApp
Facebook
Reddit
LinkedIn
Email
Link Copied!
Copy
Search Qammunity.org