how do u draw an asymtote ?
diff btwn set and interval notation? and example plz
If you want teachers to help you, I suggest you use standard English capitalization, punctuation, and spelling.
I don't need help with english, thank you. I need help with math at this time and i really don't think anyone is willing to help. I am pretty sure they don't get it since i have been posting up the same question since 4 pm today. I also don't think the teachers are that stupid that they cannot understand abbreviations. ( no offence intended)
Your problem may well be as Ms Sue has suggested that your question is incomplete, you do need help with english (sic) and on into the night. We do care but we can't help if we can't understand the question.
Here is a site that will show you how to draw an asymptote--we can't draw structures on the board. Good luck.
http://en.wikipedia.org/wiki/Asymptote
To draw an asymptote, follow these steps:
1. Understand the function: An asymptote is a line that a curve approaches but doesn't intersect. It is helpful to know the equation or the graph of the function.
2. Determine the behavior of the function: Identify any restrictions on the function or any points where the function approaches infinity or negative infinity.
3. Vertical asymptotes: Vertical asymptotes occur when the function becomes infinite. Find the values of x for which the function is undefined or approaches infinity or negative infinity. Draw vertical lines passing through those x-values.
4. Horizontal asymptotes: Horizontal asymptotes occur when the function approaches a constant value as x approaches positive or negative infinity. Identify the limiting behavior of the function as x approaches positive or negative infinity.
5. Slant asymptotes: Slant (or oblique) asymptotes occur when the degree of the numerator is one greater than the degree of the denominator. Use polynomial long division to find the quotient and remainder. The quotient will give the slant asymptote.
Difference between set and interval notation:
Set notation: In set notation, we represent a collection of numbers using braces {}. For example, the set of all even numbers can be written as {2, 4, 6, 8, ...}. We use commas to separate the elements in the set.
Interval notation: In interval notation, we represent a range of numbers using brackets [] and parentheses (). There are three types of intervals:
- Closed interval: Includes both the starting and ending points. For example, [1, 5] represents all numbers from 1 to 5, including 1 and 5.
- Open interval: Excludes the starting and ending points. For example, (1, 5) represents all numbers from 1 to 5, excluding 1 and 5.
- Half-open or half-closed interval: Includes one endpoint but excludes the other. For example, [1, 5) represents all numbers from 1 to 5, including 1 but excluding 5.
Example:
Let's say we have the inequality x ≥ 3.
Set notation: The set of all solutions can be represented as {x | x ≥ 3}, which means "the set of all x such that x is greater than or equal to 3".
Interval notation: The same inequality can be represented as [3, ∞), which means "all numbers greater than or equal to 3".