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