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What does it mean when we say that function's graph approaches infinity as it gets closer to a vertical asymptote?
Wiki User
∙ 14y ago
Definition: The line x = a is called a vertical asymptoteof the curve y = f(x) if at least one of the following statements is true:
lim(x→a) f(x) = ∞; lim(x→aâ») = ∞, lim(x→ aâº) = ∞
lim(x→a) f(x) = -∞; lim(x→aâ») = -∞, lim(x→ aâº) = -∞
In general we write lim(x→a) f(x) = ∞ to indicate that the values of f(x) become larger and larger (or "increases without bound") as x becomes closer and closer to a. (It simply express the particular way in which the limit does not exist.)
The symbol lim(x→a) f(x) = -∞ can be read as "the limit of f(x), as x approaches a, is negative infinity" or "f(x) decreases without bond as x approaches a." That is the limit does not exist.
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∙ 14y ago
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What is the term for A line that a graph approaches but does not reach It may be a vertical horizontal or slanted line?
An asymptote.
How do you find asymptotes of any function?
Definition: If lim x->a^(+/-) f(x) = +/- Infinity, then we say x=a is a vertical asymptote. If lim x->+/- Infinity f(x) = a, then we say f(x) have a horizontal asymptote at a If l(x) is a linear function such that lim x->+/- Infinity f(x)-l(x) = 0, then we say l(x) is a slanted asymptote. As you might notice, there is no generic method of finding asymptotes. Rational functions are really nice, and the non-permissible values are likely vertical asymptotes. Horizontal asymptotes should be easiest to approach, simply take limit at +/- Infinity Vertical Asymptote just find non-permissible values, and take limits towards it to check Slanted, most likely is educated guesses. If you get f(x) = some infinite sum, there is no reason why we should be able to to find an asymptote of it with out simplify and comparison etc.
What is the vertical asymptote of 4 divided by x2?
2
What is the domain of the function fx equals 3 over x plus 2?
- 2 makes this zero and provides the vertical asymptote. So, from - infinity to - 2 and from - 2 to positive infinity
What is the slope of a vertical line or division by zero?
The slopes of vertical lines and the results of divisions by 0 do not exist because there are multiple answers. A line that is vertical can have a slope of infinity or negative infinity. Same with division by zero. Picture the graph 1/x. As the graph approaches zero from the left, it goes toward negative infinity, then jumps to positive infinity. There are two answers, and neither of them are real numbers. The limits do exist though. The limit of 1/x as x approaches zero from the left is negative infinity. and the limit as it approaches the right is positive infinity.
When a vertical asymptote is reflected over the x axis what does it become?
It remains a vertical asymptote. Instead on going towards y = + infinity it will go towards y = - infinity and conversely.
How do you find vertical asymptote?
One way to find a vertical asymptote is to take the inverse of the given function and evaluate its limit as x tends to infinity.
What is A line that a graph approaches but does not reach It may be a vertical horizontal or slanted line?
It is an asymptote.
What is the term for A line that a graph approaches but does not reach It may be a vertical horizontal or slanted line?
An asymptote.
All rational functions have more than one vertical asymptote?
false
Some rational functions have more than one vertical asymptote?
yes
How do you find asymptotes of any function?
Definition: If lim x->a^(+/-) f(x) = +/- Infinity, then we say x=a is a vertical asymptote. If lim x->+/- Infinity f(x) = a, then we say f(x) have a horizontal asymptote at a If l(x) is a linear function such that lim x->+/- Infinity f(x)-l(x) = 0, then we say l(x) is a slanted asymptote. As you might notice, there is no generic method of finding asymptotes. Rational functions are really nice, and the non-permissible values are likely vertical asymptotes. Horizontal asymptotes should be easiest to approach, simply take limit at +/- Infinity Vertical Asymptote just find non-permissible values, and take limits towards it to check Slanted, most likely is educated guesses. If you get f(x) = some infinite sum, there is no reason why we should be able to to find an asymptote of it with out simplify and comparison etc.
What is the vertical asymptote of 4 divided by x2?
2
What is the domain of the function fx equals 3 over x plus 2?
- 2 makes this zero and provides the vertical asymptote. So, from - infinity to - 2 and from - 2 to positive infinity
What is the slope of a vertical line or division by zero?
The slopes of vertical lines and the results of divisions by 0 do not exist because there are multiple answers. A line that is vertical can have a slope of infinity or negative infinity. Same with division by zero. Picture the graph 1/x. As the graph approaches zero from the left, it goes toward negative infinity, then jumps to positive infinity. There are two answers, and neither of them are real numbers. The limits do exist though. The limit of 1/x as x approaches zero from the left is negative infinity. and the limit as it approaches the right is positive infinity.
True or False if a rational function Rx has exactly one vertical asymptote then the function 3Rx should have the exact same asymptote?
It will have the same asymptote. One can derive a vertical asymptote from the denominator of a function. There is an asymptote at a value of x where the denominator equals 0. Therefore the 3 would go in the numerator when distributed and would have no effect as to where the vertical asymptote lies. So that would be true.
Can the graph of a polynomial function have a vertical asymptote?
no
