Consider the function below. f(x) = (x^2)/(x−9)^2 (a) Find the vertical and horizontal asymptotes. x=? y=? (b) Find the interval where the function is increasing. (Enter your answer using interval notation.) Find the interval where the function is decreasing. (Enter
119,928 results
Math
All rational functions can be expressed as f(x) = p(x)/q(x), where p and q are __________ functions and q(x) ≠ 0. A. horizontal asymptotes B. polynomial C. vertical asymptotes D. slant asymptotes Is the answer D. vertical asymptotes?

algebra
Find an equation of a rational function that satisfies the following conditions: • Vertical asymptotes: x = −3 • Horizontal asymptote: y=3/2 • x intercept: 5 • Hole at x =2

m240
All rational functions can be expressed as f(x) = p(x)/q(x), where p and q are __________ functions and q(x) ≠ 0. A. horizontal asymptotes B. polynomial C. vertical asymptotes D. slant asymptotes My answer is B is this correct.

calculus
Find a formula for a function that has vertical asymptotes at x=7 and x=9 and a horizontal asymptote at y=7

Calculus
If f is a continuous function with even symmetry and lim x→∞ f(x)=10, which of the following statements must be true? I. lim x→∞ f(x)=10 II. there are no vertical asymptotes III. The lines y=10 and y= 10 are horizontal asymptotes a) I only b) II

math
what is a function that Contains no vertical asymptotes but has a hole at x=2 and another function that contains a horizontal asymptote of 1, vertical asymptotes of 2 and 3, and a hole at x=4.

Math
Write the equation of the rational function that passes through the points (0,0) and (4,8/7), has the xaxis as a horizontal asymptote, and has 2 vertical asymptotes at x=3 and x=3.

PreCalculus
I want to learn how to find the domain, holes, xintercepts, y intercepts, vertical asymptotes, and horizontal asymptotes of a rational function. I know it is against the rules in jiskha to do the homework for the students but if I have been looking over

precalculus
Find an equation for a rational function with the following properties: vertical asymptotes at x=1 and x=−9 zero at x=11 f(0)=15 horizontal asymptote at y=0 please check my work thanks I got: 15(x11)^2/(x1).(x+9)

Math
f(x) is a linear function which is increasing for XER. a) Will the reciprocal function be increasing or decreasing? b)Will there ever be any horizontal asymptotes for the function? If so, where? c)Will there ever be any horizontal asmptotes for the

Math
Verify these answers :] Would be thankies~ 1. Determine the intervals in which the reciprocal function of f(x)= x^2+1 is increasing. a) (0,∞) b) (∞, 0) c) (∞,∞) d) (1,∞) Answer: D  2. Determine the point(s)

Algebra
Find a rational function that satisfies the given conditions. Vertical asymptotes x=2,x=7 Horizontal asymptote y=7/2 xintercept (−5, 0)

Gr.11  Rational functions graphing.
1. Identify a rational function whose graph is a horizontal line except for two holes. Graph the function. 2. Identify a rational function who graph lies entirely above the xaxis and has a single vertical asymptote. Graph the function. 3. Identify a

****college algebra…radical functions****
Create a rational function such that the graph of has vertical asymptotes at x=5 and x= 7, a hole at x=2 , and a horizontal asymptote at y = 14. By creating a rational function, you are to write rule for this function. There are many correct solutions

Geomatry
For each of the rational functions find: a. domain b. holes c. vertical asymptotes d. horizontal asymptotes e. oblique asymptotes f. yintercept g. xintercepts 1. f(x)= x^2+x2 / x^2x6

math
Find a formula for a function that has vertical asymptotes x = 3 and x = 6 and horizontal asymptote y = 3.

Calculus
Let f(x)=(4x^2 7x +2)/(x^2 16x +63) Find the equations of the horizontal asymptotes and the vertical asymptotes of f(x). If there are no asymptotes of a given type, enter NONE. If there is more than one asymptote of a given type, give a comma separated

calculus
consider the function y=(ax+b)/(cx+d), where a,b,c,and d, are constants, a,c cannot equal 0. determine the horizontal and vertical asymptotes of the graph

algebra
For each of the rational functions find: a. domain b. holes c. vertical asymptotes d. horizontal asymptotes e. oblique asymptotes f. yintercept g. xintercepts 1. f(x)= x^2+x2 / x^2x6

Math 111 URGENT
Find the vertical asymptotes of the following function: f(x)={x3}/{(x3)(x^24)}. The equation(s) of the vertical asymptote(s) of f is/are___ & ____

College Algebra HELP
Use the seven step method described in the book to graph the following rational function f(x)=(2x^2+x3)/(2x^27x) 1) Determine the symmetry of the function 2) Find the yintercept 3) Find the xintercept 4) Find the vertical asymptotes 5) Find the

Math (algebra)
Question: Create a rational function f(x) such that the function has: 2 vertical asymptotes 1 hole 1 positive horizontal asymptote

APCalculus
For the function y=2sin(x)cos^2(x) on [0, 2pi] find the following: Domain x and y intercepts Vertical asymptotes Horizontal asymptotes Symmetry F'(x) Critical numbers Increasing f(x) Decreasing f(x) Extrema F"(x) Possible points of inflection Concave up

Math  Domain and Asymptotes
Given the following rational function: f(x) = (x^2 + 6x  8) / (x – 5) (a) state the domain. (b) find the vertical and horizontal asymptotes, if any. (c) find the oblique asymptotes, if any.

MATH
Create a rational function with a linear binomial in both the numerator and denominator. Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x and yintercepts on your graph. Label the asymptotes and

Precalc
Write an equation for a rational function with: Vertical asymptotes at x=1 and x=4 x intercepts at x=6 and x=6 Horizontal asymptote at y=2 y=

Math
Determine the holes, vertical asymptotes and horizontal asymptotes of the rational function. y=3x^2+10x8/x^2+7x+12 Can you also show your work. I need to do corrections. I have a 68 I just need to get to a 70. This would mean so much to me if anybody

Harrisburg Area Community College
find the equation of a rational function that passes through (0,1) and (2,1), has the x axis as a horizontal asymptote, and has two vertical asymptotes at x=3 and x=3

college algebra
find the vertical, horizontal, oblique asymptotes, if any, for the given rational function. R(x)=10x^2+19x15  2x+5 please show how you arrived with the answer! thank you

precalculus
given the following rational function f(x)= x^2+5x7 / x4 state domain, find vertical, horizontal and oblique asymptotes if any. I found the domain to be (inf.,4)U(4, inf.) and vertical asymptote at x=4 am I right? can someone help me with the rest?

Algebra
Find the vertical, horizontal, and oblique asymptotes, if any, for the following rational function. T(x)=x^2/x^4256

college algebra
given the following rational, find the horizontal asympotes the vertical asymptotes if any and the oblique asymptotes if any f(x)=x^2x2 over 2x^2x10

Calculus
Find all vertical and horizontal asymptotes of the graph of the function. (Enter your answers as a commaseparated list.) f(x) = 5 − 3x/5 + 8x

Mathprecalc
Is it possible to find a rational function that has xintercepts (2,0) and (2,0), but has vertical asymptote x=1 and horizontal asymptote of y=0? The horizontal asymptote and the xintercepts parts stump me. If you can't reach y=0, then how can you get

algebra 21
What are the vertical and horizontal asymptotes for the function mc0171.jpg?

Math
The following rational function describes blood concentration of a certain drug taken via IV over time, find a. the horizontal or oblique asymptotes b. the vertical asymptote c. describe their possible meanings f(x)= x+1/x

precal
Find an equation for a rational function with the following properties: vertical asymptotes at x=5 and x=9 zero at x=14 horizontal asymptote at y=9 Leave your answer in factored form. my answer: f(x)=9(x14)^2/(x5)(x9)...is this correct? thanks

Algebra 2
Identify all horizontal and vertical asymptotes of the graph of the function. f(x)=x^2/x^24 I know the vertical asymptotes are x=2 and x=2, but how do I find the horizontal asymptotes?

Algebra
Determine the holes, vertical asymptotes and horizontal asymptotes of the rational function y=(3x^(2)+8x10)/(x^(2)+7x+12) Hole: Vertical Asymptote: Horizontal Asymptote:

math calculus
For the function: f(x)= 2+xx^2/ (x1)^2 ; f'(x)= x5/(x1)^3 ; f''(x)=2x14/(x1)^4 a)find vertical and horizontal asymptotes. Examine vertical asymptote on either side of discontinuity. b)find any local extrema c)find points of inflection

College Algebra
1.Use completing the square to describe the graph of the following function. Support your answer graphically. f(x) = 2x^2 + 4x + 5 2. Find the vertical, horizontal, and oblique asymptotes, if any, for the following rational function. R(x) = 5x/x+7 The

MATHS Calculus
Find the vertical and horizontal asymptotes of the function F(x)=x=(√9x^2)/(2x+1)

precal
Find an equation for a rational function with the following properties: vertical asymptotes at x=2 and x=−8 zero at x=17 horizontal asymptote at y=0 is it (x17)^2/(x+2).(x+8)

math
g(x)=(2x^3+x^218x9)/(x^2+x6) A. Find the vertical asymptotes. b. find any holes. c. find any oblique or horizontal asymptotes. d. find if the graph crosses the oblique or horizontal asymptote.

Math
A rational function g has the lines x=2 and x=2 as vertical asymptotes, the line y=4 as a horizontal asymptote, and numbers 3 and 1 as zeros. Find a formula for g(x). So I got g(x)=(4x^216x+12)/(x^24) Is this correct

Pre cal
Determine all xintercepts, vertical asymptotes, horizontal asymptotes, and removable discontinuities of f (x)=(x^2x6)/(x^34x).

Math
give the domain of the function and identify any vertical or horizontal asymptotes. g(x)= 1 / x3 + 1 My answer was x = o and y=3 but this was wrong. Please explain!!

math
𝑦 = (3x^2)/(x^24) Determine equation of vertical asymptotes. For vertical asymptotes, investigate function values on either side of the asymptote I know that the vertical asymptotes is located at x = 2, 2, but I don't understand what the questions

precalculus
(A) find the domain of the function, (B) decide if the function is continuous, and (c) identify your horizontal and vertical asymptotes. F(x)= (3x^2+1)/(x^2+x+9) Find the zeros (if any) of the rational function. G(x)= (x^38)/x^2+4 H(x)=5 + 3/(x^2+1) G(x)=

precalculus
(A) find the domain of the function, (B) decide if the function is continuous, and (c) identify your horizontal and vertical asymptotes. F(x)= (3x^2+1)/(x^2+x+9) Find the zeros (if any) of the rational function. G(x)= (x^38)/x^2+4 H(x)=5 + 3/(x^2+1) G(x)=

Calculus (pleas help!!!)
Please answer the following questions about the function f(x)=e^(0.5x^2) Instructions: If you are asked to find x or yvalues, enter either a number, a list of numbers separated by commas, or None if there aren't any solutions. Use interval notation if

Calculus (urgent!!)
Please answer the following questions about the function f(x)=e^(0.5x^2) Instructions: If you are asked to find x or yvalues, enter either a number, a list of numbers separated by commas, or None if there aren't any solutions. Use interval notation if

Calculus (pleas help!!!)
Please answer the following questions about the function f(x)=e^(0.5x^2) Instructions: If you are asked to find x or yvalues, enter either a number, a list of numbers separated by commas, or None if there aren't any solutions. Use interval notation if

PRECALC
I am given the rational function: f(x)= (x^3  1) / (x^2  4) I found that the domain is all real numbers except x= plus or minus 2 , I also found that the x intercept is x=1, however I do not get how to find: the yintercet , or identify the Horizontal,

algebra
Create a rational function with a linear binomial in both the numerator and denominator. Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x and yintercepts on your graph. Label the asymptotes and

ALGEBRA
Create a rational function with a linear binomial in both the numerator and denominator. Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x and yintercepts on your graph. Label the asymptotes and

Math
Create a rational function with a linear binomial in both the numerator and denominator. Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x and yintercepts on your graph. Label the asymptotes and

ALGEBRAA
Create a rational function with a linear binomial in both the numerator and denominator. Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x and yintercepts on your graph. Label the asymptotes and

pre calculus
given the following rational function a. state the domain b. find the vertical and horizontal asymptotes if any c. find the oblique asymptote f(x) = x^2 + 7x + 5 / x + 8

AP Calculus
Consider the function f(x)= abs(x)(x3)/9x^2 a) what is the domain of f? What are the zeros of f? b) find all nonremovable discontinuities of f c) determine all vertical and horizontal asymptotes of f

precalc
What function has 2 vertical asymptotes at x=3/2 and x=3/2 and a horizontal asymptote at 3/4? I know that the coefficients of the rational function are 3 and 4 but I don't know how to figure anything else out.

college algebra
Given the following rational function, find: A. horizontal asymptotes B. vertical asymptote(s), if any C. oblique asymptote(s), if any f(x)=x^2x2/2x^2x21

horizontal asymptote
Find the horizontal asymptotes of the function's graph y = 200 / (1+10e^(0.5x)) If you let x > minus infinty the exponential tends to zero and the function approaches 200. If x > infinity then the exponential becomes infinite and therefore the limit is

Seven step method
Use the seven step method described in the book to graph the following rational function f(x)=(2x^2+x3)/(2x^27x) 1) Determine the symmetry of the function 2) Find the yintercept 3) Find the xintercept 4) Find the vertical asymptotes 5) Find the

Math
find a rational function that satisfies the given conditions vertical asymptotes x=6,x=7 horizontal asymptotes y=10/9 x intercepts (6,0)

PreCalc
Consider the function(7+15x^2)/(10x^2+9x+10). Find the function's domain and identify any horizontal and vertical asymptotes Please Help!

PreCal
use a graphing calculator to obtain the graph of the function. What do you observe about its asymptotes? g(x) = 4 [x2] / x + 1 My answer was there are two horizontal asymptotes. My teacher said that there are two asymptotes but she wants me to find the

College algebra
Find the vertical, horizontal, and qblique asymptotes, if any, for the following rational function. T(x)=x^2/x^4256

math please
1.Give a linear function with its zero at x=a, what is the equation of the vertical asymptote of its reciprocal function? 2.Give a quadratic function with its zeros at x=a and x=b, what are the equations of the vertical asymptotes of its reciprocal

graph from asymptotes
Is it possible to roughly sketch a graph(without plotting the points) from the asymptotes of a rational function? Is yes, what are the rules? For example, if I have to sketch a graph of y = (2x^2+10x12)/x^2+x6), how do I do it? I got the vertical

Calculus
A rational function g has the lines x=2 and x=2 as vertical asymptotes, the line y=4 as a horizontal asymptote, and numbers 3 and 1 as zeros. Find a formula for g(x).

math help please...
1.Explain how to find the equation of the vertical asymptotes of a reciprocal function. 2.The reciprocal of a linear function and a quadratic function have the same horizontal asymptote. What is its equation? 3.Explain how to use end behaviour to find the

mathalg
11. What are the horizontal and vertical asymptotes for the rational function y = 4x /(x1)?: x = 0, y = 0 x = 1, y = 4 x = 4, y = 1 x = 1, y = 0

PreCalc
1/x3 +1 Use a graphing utility to obtain the graph of the function. Give the domain of the function and identify any vertical or horizontal asymptotes.

Calculus (Reiny or MathMate)
A rational function g has the lines x=2 and x=2 as vertical asymptotes, the line y=4 as a horizontal asymptote, and numbers 3 and 1 as zeros. Find a formula for g(x). So I got g(x)=(4x^216x+12)/(x^24) Is this correct

Calculus
A rational function g has the lines x=2 and x=2 as vertical asymptotes, the line y=4 as a horizontal asymptote, and numbers 3 and 1 as zeros. Find a formula for g(x). So I got g(x)=(4x^216x+12)/(x^24) Is this correct Math Mate?

Algebra
List all asymptotes (both horizontal and vertical) of the rational function: f(x)=(10x−3)/(8−7x)

Math
The asymptotes of the function g(x)=(x+2)/(x^2+2x3) are... a. vertical: x=2, x=1; horizontal: y=0 b. vertical: x=3, x=1; horizontal: y=0 c. vertical: x=2, x=3; horizontal: y=0 d. vertical: x=3, x=1; horizontal: none

math
5. State a rational function that satisfies all of the following: The y – intercept is 24 There is a horizontal asymptote at y = 3 There are vertical asymptotes at x = 1 and x = 4

calculus
Give a reasonable sketch, on the axes provided, of the graph of the function x/(x^21)^1/2 showing all characteristics. Use the following pieces to justify your sketch. a) Domain ? b) coordinates x and y intercepts ? c) Symmetry ? is the function odd,

calculus
final question Consider the function F(x)=3x^45x+3 / X^4+1 Find: Domain Vertical,horizontal,or slant asymptotes xintercept(s) yitercept(s) symmetry(respect to x, yaxis or orgin) F’ (x) Critical numbers F” (x) Possible points of inflection

calculus
For the function r(x)=x3+6x2x2−36, find the following. a. the y  intercept b. the x  intercepts c. all horizontal asymptotes. y = d. all vertical asymptotes. x =

Math
What is meant by the terms vertical and horizontal asymptotes Here is a nice graph with vertical and horizontal asymptotes. THe dotted lines are the asymptotes. http://www.mathnstuff.com/math/spoken/here/2class/300/fx/library/234/n1oxp4.gif

Math Functions
f(x)= 3x+2/2x+4 graph the function horizontal and vertical asymptotes. Show the table. I found the horizontal and vertical asymptotes, but im confused on how to do a table

calculus 1
how do i find all vertical and horizontal asymptotes for the function y= 3x^28x+25/x^2+7x18

calculus
The following rational function describes concentration in blood of a certain medicine taken once depending on time, find: A.the horizontal asymptote(s) B.the vertical asymptote(s) C. describe their possible meanings Horizontal asymptote is y=100 vertical

Math
what rational expression will fit each of the descriptions? a. Contains 2 vertical asymptotes. b. Contains a Horizontal asymptote of 3. c. Contains no vertical asymptotes but has a hole at x=2. d. Contains a horizontal asymptote of 1, vertical asymptotes

PreCal
State the transformations. Identify holes, vertical asymptotes, and horizontal asymptotes of each. (I'm fine with the asymptotes, just need help with stating the trandformations) f(x)= (3x+9)/(x+2)

Math  asymptotes
Identify all asymptotes. 1. y= 1 / 2√x^2  3x the asymptotes I got were: vertical: 1 & 4 horizontal: 0 Is this it or are there more? 2. y= x^32x / x^2 + 1 I believe there are no asymptotes? Is this correct?

Calculus
Sketch the graph of f(x)=x^4 + 4x^3  16x + 16: Find the critical points, concave up/down, inflection points, vertical asymptotes and horizontal asymptotes.

Calculus
Create a function that has a graph with the following features: Two vertical asymptotes: x=1, x=3. One horizontal: y = 1. And x intercepts= 2, 4 how about f(x) = ((x+2)(x4))/((3x)(x1)) ?

calculusplease check
analyze the graph of the function f(x)=x^2+x90/x+3 a. what is the domain? I think it is x‚3 (‡,3)(3‡) b. what is the equation of the vertical asymptote? is it x= 3 c. what is the horizontal asymptotes? none

calculusplease check
analyze the graph of the function f(x)=x^2+x90/x+3 a. what is the domain? I think it is x‚3 (‡,3)(3‡) b. what is the equation of the vertical asymptote? is it x= 3 c. what is the horizontal asymptotes? none

Math
Analyze the function algebraically. List its vertical asymptotes, holes, yintercept, and horizontal asymptote, if any. q(x)= 4/x2 vertical asymptote= hole= horizontal asymptote= yintercept=

APCalculus
For the function y=42x^2+1/6x^4 find the following: Domain x and y intercepts Vertical asymptotes Horizontal asymptotes Symmetry F'(x) Critical numbers Increasing f(x) Decreasing f(x) Extrema F"(x) Possible points of inflection Concave up Concave down

Algebra2
determine if the hyperbola is vertical or horizontal then find the vertices foci and asymptotes y^2/25x^2/100=1 My answers Horizontal?

Calc
f(x) = x^2 / (x  7)^2 (a) Find the vertical and horizontal asymptotes. x= y= (b) Find the interval where the function is increasing. Find the intervals where the function is decreasing. (Enter the interval that contains smaller numbers first.) (c) Find

Math
(x^2+x2) / (x^23x4) X and y intercepts? Horizontal Asymptotes? Vertical Asymptotes?

calculus
find all horizontal and vertical asymptotes of f(x)=2x^2+7x+12/2x^2+5x12

Calculus 1
Find the horizontal and vertical asymptotes of (3x^248)/(x^23x+10)