# math(precalculus)

posted by .

Write the equation of a Rational Function satisfying given conditions.

Has vertical asymptotes located at x-2 and x=-1
Has a horizontal asymptote located at y=0(x-axis)
y-intercept:(0,2) x-intercept (4,0)

R(x)= ???

what I did is,
R(x)= ax+b/c(x-2)(x+1)
then plug in (0,2), b=-4c
plug in(4,0), a=c

• math(precalculus) -

You don't need any c. It can be absorbed into a and b.

Actually, you have solved the problem. Pick any value for c, and plug it in. As long as a=c and b=-4c, R(x) will work. So, make things easy. Let c=1.

As I worked it out,

R(x) = ???/(x+1)(x-2)

Since y=0 is the asymptote, you know that the degree of the numerator is less than the denominator. So,

R(x) = (ax+b) / (x+1)(x-2)
Now, with the intercepts, you know that

b/(1)(-2) = 2, so b = -4
a(4)+b = 0, so 4a-4=0, so a=1

R(x) = (x-4)/(x+1)(x-2)

## Similar Questions

1. ### Math

Analyze the function algebraically. List its vertical asymptotes, holes, y-intercept, and horizontal asymptote, if any. q(x)= -4/x-2 vertical asymptote= hole= horizontal asymptote= y-intercept=
2. ### Precalculus

Write an equation for rational function with given properties. a) a hole at x = 1 b) a vertical asymptote anywhere and a horizontal asymptote along the x-axis c) a hole at x = -2 and a vertical asymptote at x = 1 d) a vertical asymptote …
3. ### math

how do you create a function that has a graph with the given features: a. A vertical asymptote at x=2; a horizontal asymptote at y=0; no x-intercept; y-intercept is 3 please help.
4. ### math

how do you create a function that has a graph with the given features: a. A vertical asymptote at x=2; a horizontal asymptote at y=0; no x-intercept; y-intercept is 3

write an equation for a rational function whose graph has all of the indicated features: -vertical asymptote with equation x=3 -horizontal asymptote with equation y=2 -hole at x=1 no x intercept thank you
6. ### 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
7. ### PreCalculus

State the Vertical Asymptote, Horizontal Asymptote, domain, range, x intercept and y intercept for the following Function. y= (5-x)/(x+3) I already know that the Vertical asymptote is -3, so that means the domain is everything except …
8. ### Rational Functions

Write an equation for a rational function whose graph has the following properties: x-intercept of 3 y-intercept of -3 vertical asymptote of x=-2 horizontal asymptote of y=2
9. ### Math

Write the equation of a rational function in the form of 𝑓(𝑥) = 𝑎𝑥+𝑏/𝑐𝑥+𝑑 if the vertical asymptote is x =5, the horizontal asymptote is y=2, the x-intercept is (-1/2 …
10. ### Algebra

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

More Similar Questions