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Question 7J0p(0) Find all asymptotes ard intercepts of the following furc tion; Find the inverse function J()...

Question

Question 7J0p(0) Find all asymptotes ard intercepts of the following furc tion; Find the inverse function J()

Question 7 J0p (0) Find all asymptotes ard intercepts of the following furc tion; Find the inverse function J()



Answers

Find all vertical asymptotes and horizontal asymptotes (if there are any). $$f(x)=\frac{7 x^{3}+1}{x+5}$$

All right. The functional given here is F vax is equal to shoe minus X cube, and that is all divided by two X minus seven e. And where to find the vertical and horizontal ass symptoms. So, um well, forever glass and felt, um, the vertical Lassen talks are just wherever the denominator is equal to zero. So we have two X minus seven Weakness. Take two X minus seven, and set that equal to zero and then find out whatever this is equal to zero. That is going to be where the vertical Adam is gonna be. So you saw this for X, so we just moved seven over. I mean, two X is equal to a positive seven, adding seven to both sides of the body. By two. We get X is equal to seven abs. So to be the vehicle ass in tow at X is equal to seven haps exiting the seven halves. The denominator is equal to zero. Okay, so you have working at X equal seven halves now for a horizontal Assam told. Well, we have to know if the degree of the numerator is greater than or less than the degree of the denominator. But where this function is set up was kind of hard to tell, because I have I don't have my I should have a right, my basically my highest power first and then hair of decreasing powers. Right now I have tu minus X cube on top. I can rewrite that as minus X cube plus two, right, And then that is over two x minus seven. And now it's easier to see that the degree of the numerator is three. Degree of the nominator is one. So therefore the degree of the numerator is greater than the degree of the nominator. When that happens, we do not have any, um, horizontal asking toes. So there are no words on that. That's no right.

This question asked us to simplify the function 21 minus seven X over three X minus nine. First, let's note any discrepancies in its domain, so this function will be undersigned, but three X minutes. Nine. It's denominator is equal to zero, which occurs when X is equal to three. That in mind, we go ahead and simplify function so we can pull out a seven as a common factor. And the numerator they were left with three minus x denominator. We can pull out the three x minus nine. How sorry X minus three. Since you might, it's nine. Originally, it's minus three three months. Axes just negative. X minus three. So this simplifies Teoh negative 7/3. So it's discrepancy in the domain isn't really important.

We have it off. X is equal toe explosive and divide by two minus X. Since the denim enter off, this function becomes zero at X quarto. We say that X equal to does not belong to the domain off this function. And we can say that the domino this funds and it explodes to minus infinity, toe to union to infinity and the vertical of some sort off This function is X equals toe to

This question is asking us to find all horizontal and vertical symptoms, if any. Okay, What we know is that an irrational function vertical access codes for the zeroes of the denominator. So if we have explains to reset this equal to zero and we have four X plus seven for this equal to zero, they can actually solved. We get access to an ex is negative seven divide before these are vertical ascent tuts now horizontal ass and trucks are determined when we look at the degree of the leading term of the numerator and regards to the denominator so we can see the degrees are the same, they are equivalent. Therefore, we know the ratio of the coefficients is the horizontal accent. Oh, so to over four is 1/2 So 1/2 is why is in this context the horizontal acid took as we established X equals two and X equals negative seven. Divide by four are horizontal. Are vertical ascent tips


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