## anonymous one year ago Will METAL!! For the given function, find the vertical and horizontal asymptote(s) (if there are any). f(x) = the quantity x squared plus three divided by the quantity x squared minus nine A) x = 3, x = -3, y = 1 B) x = 9, y = 3 C) None D) x = 9, y = 1

1. anonymous

|dw:1443864761554:dw|

2. anonymous

will metal @satellite73

3. Koikkara

4. Koikkara

$$\color{blue}{\huge\tt{Nice~}}$$ $$\huge\mathcal{to~meet~}$$ $$\color{red}{\huge\tt{You~!}}$$

5. mathmate

Horizontal asymptote is y=k, if the leading coefficient of the numerator divided by the leading coefficient of the denominator is a constant k. Example: y=(2x-3)/(x-2), k=2x/x=2, so horizontal asymptote is at y=2. In this case, x^2/x=x, so the asymptote is a slanting one, y=x.

6. Nnesha

there is a mistake in ur question i think it's x^2 -9 |dw:1443875623116:dw|

7. Nnesha

bec ~if the highest degree of the numerator is greater than the denominator then No horizontal asy. $\color{reD}{\rm N}>\color{blue}{\rm D}$ example $\large\rm \frac{ 7x^\color{ReD}{3} +1}{ 4x^\color{blue}{2}+3 }$ use the example provided by math to find horizontal asy.

8. anonymous

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. f(x) = quantity x minus seven divided by quantity x plus two. and g(x) = quantity negative two x minus seven divided by quantity x minus one.

9. mathmate

Example: f(x)=log(x) g(x)=e^x f(g(x))=log(e^x))=x, so g is the inverse of f (and vice versa) Another example f(x)=2x+3 g(x)=(x-3)/2 f(g(x))=2((x-3)/2)+3=x-3+3=x g(f(x))=((2x+3)-3)/2=2x/2=x so g is the inverse of f (and vice versa)

10. anonymous

@ribhu

11. anonymous

ok now can you draw out the problem you wrote down on here.

12. ribhu

A

13. ribhu

its very difficult..

14. ribhu

you can take the solution from the pic..

15. mathmate

Do you mean this? "f(x) = quantity x minus seven divided by quantity x plus two. and g(x) = quantity negative two x minus seven divided by quantity x minus one." f(x)=(x-7)/(x+2) g(x)=(-2x-7)/(x-1) Except that the question should have read: "f(x) = quantity x minus seven $$\color{red}{all}$$ divided by quantity x plus two. and g(x) = quantity negative two x minus seven $$\color{red}{all}$$ divided by quantity x minus one." It shows that the person who made up the problem does not work daily with algebra.