PLEASE help me with graphs with rational funtions?1?!


Question: PLEASE help me with graphs with rational funtions?1?
Dont make rude comments. If you are good at precalculus then please help. Yahoo answers are to help others. So please help me out!! I suck at maths.

1. What is the domain of the function below?
f(X)=1/x^2-9?

2. Identify the vertical and horizontal asymptotes of the funtion below?
f(x)=1-1/x-1

8. What are the x-itercepts for the funtion below?
f(x)=5/x+4-x

7. What is the x-intercept for the function below?
f(x)=5 (2/x-1/x-2)

6. I dentify the vertical and horizonal asymptotes of the funtion below?
f(x)=1/x+4+2

5. What is the domain of the function below?
f(x)=4-x/x+1

i am sorry baout mixing the problems, but i really need your help. thanks

i want 100 percent accurate answers if your smart enogh to do all the problems. sorry for the spellings.

Answers:

You really should restrict your questions to 1 or 2 per post.
These could easily have been split into 3 posts, since there are 3 topics.

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Domain is all values of x that do not create undefined result, such as square root of negative number or dividing by 0

1. There is no square root, but we do have denominator: x^2 - 9

We find values of x that make denominator = 0
x^2 - 9 = 0
x^2 = 9
x = -3, 3

Domain: all real numbers except x = 3, x = -3
{x ∈ ? | x ≠ -3, x ≠ 3}


5. Same method: x ≠ 1

=========================

Vertical asymptotes occur when x approaches a value that makes denominator = 0

2. f(x) = 1 - 1/(x-1)

Denominator = 0 when x = 1
Vertical asymptote: x = 1

Horizontal asymptotes are found by finding limit of f(x) as x approaches ±∞
lim[x→∞] 1 - 1/(x-1) = 1 - 0 = 1
lim[x→-∞] 1 - 1/(x-1) = 1 + 0 = 1
Horizontal asymptote: y = 1


6. f(x) = 1/(x+4) + 2

Denominator = 0 when x = -4
Vertical asymptote: x = -4

lim[x→∞] 1/(x+4) + 2 = 0 + 2 = 2
lim[x→-∞] 1/(x+4) + 2 = -0 + 2 = 2
Horizontal asymptote: y = 2

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To find x-intercept, find x so that f(x) = 0

7. f(x) = 5 (2/x - 1/(x-2))

5 (2/x - 1/(x-2)) = 0
2/x - 1/(x-2) = 0
2/x = 1/(x-2)

Cross multiply
2(x-2) = 1x
2x - 4 = x
2x - x = 4
x = 4

x-intercept is (4, 0)


8. f(x) = 5/(x+4) - x

5/(x+4) - x = 0
5/(x+4) = x
5 = x(x+4)
5 = x^2 + 4x
x^2 + 4x - 5 = 0
(x + 5)(x - 1) = 0
x = -5, x = 1

x-intercepts: (-5,0) and (1,0)

=========================

So next time, you should only post 1 or 2 questions at a time. Also, use brackets to reduce confusion. I just hope I got all the functions above correct, otherwise my results will be wrong.




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