How do you graph f(x)=2x−1/x^3−9x using holes, vertical and horizontal asymptotes, x and y intercepts?
tuzkutimonq4
Answered question
2022-09-11
How do you graph using holes, vertical and horizontal asymptotes, x and y intercepts?
Answer & Explanation
FIRST thing we ALWAYS do is making the function easier:
because
Now we can "easily" see that x MUST NOT be 0,3,-3 because we know that we must not divided by 0.
We can also see that (2x−1=0) if
vertical asymptotes:
Therefore we now know that the function has 3 vertical asymptotes (we get them when x=0 in the "down side of the equation"):
x=0
x=3
x=−3
horizontal asymptotes:
(I don't know if you know how to use lim so I will explain in an alternative way)
horizontal asymptotes is a question of a kind of "What does the function "act" when x is REALLY HUGE (and/or negative HUGE)?
To solve it easily, lets check with a calculator what happens when x comes is really big, for example I will check the positives:
So, the function goes to y=0 for very big x-es.
On the same way, we can chek the very negative x-es:
So, in that case, the function goes to y=0 for very negative big x-es.
therefore, the horizontal asymptote is:
y=0
x and y intercepts:
Now that we have an "easier" function:
We check both "x=0" and y=0":
But we already knew it because x=0 is one of ours' vertical asymptotes...
Now lets check what if what is x?
(for x in not 1,3,-3)
So we have only one point
Do you have a similar question?
Recalculate according to your conditions!