algebra

Describe the vertical asymptote and hole for the graph of (x^2+x-6)/(x^2-9).
a. asymptote: x=2; hole: x=-3
b. asymptote: x=3; hole: x=2
c. asymptote: x=-3; hole: x=3
d. asymptote: x=3; hole: x=-3

I know that it has to either be b or d because the asymptote is x=3. Can someone please help with the rest?

1. 👍
2. 👎
3. 👁
1. (x^2+x-6)/(x^2-9) = (x+3)(x-2) / (x+3)(x-3)

so there is a hole at x = -3, where y = 0/0 (undefined)
Everywhere else, y = (x-2)/(x-3) which has
zero at x=2
asymptote at x=3

so, D

1. 👍
2. 👎

Similar Questions

1. 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

2. Math

Give an example of a rational function that has vertical asymptote x = 3 and x = -3, horizontal asymptote y = 2 and y-intercept is (0, 4)

3. 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

4. Pre Cal

which of the following best describes the behavior of thre function f(x)=(x^2-2x)/(x^2-4) at the values not in its domain? a) one vertical asymptote, no removable discontinuities b) 2 vertical asymptotes c) two removable

1. Math

State an equation of a rational function that satisfies the given conditions: vertical asymptote at x=5, horizontal asymptote at y=-3, and x-intercept is 5/2. Need help solving.

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

3. Math

If x=1 is the vertical asymptote and y=-3 is the horizontal asymptote for the graph of the function f which of the following could be the equation of the curve A.f(x)=(-3x^2)/(x-1) B.f(x)=-3(x-1)/(x+3) C.f(x)=-3(x^2-1)/(x-1)

4. Mathematics

A rational function, R(x) has the following characteristics: a vertical asymptote at x = 3, a horizontal asymptote at y = 2, and a hole at (2, −2). Sketch the function and determine what it could be using the following steps:

1. Algebra

Enter the equations of the asymptotes for the function f(x) . f(x)= −(2/x+4) − 6 Vertical Asymptote: ? Horizontal Asymptote: ?

2. Math

Write an equation for a rational function whose graph has all of the indicated features. x - intercept of -4 y - intercept of -2 vertical asymptote with equation x = 2 horizontal asymptote with equation y = 1

3. Math

20. (4 points) 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-intercepts

4. Math

Write a rational function satisfying the following criteria. vertical Asymptote: x=-1, slant asymptote: y=x+2, zero of the function: x=3 I had f(x)=x^2+3x+2/x+1, that only works for the asymptotes and not the zero can someone