how do u draw an asymtote ?
diff btwn set and interval notation? and example plz
To draw an asymptote, you need to follow these steps:
1. Determine the function: Identify the equation or function for which you want to draw the asymptote.
2. Find the domain of the function: Determine the values of x for which the function is defined.
3. Identify vertical asymptotes: Vertical asymptotes occur when the function approaches infinity or negative infinity as x approaches a specific value. To find them, look for values of x for which the denominator of a rational function is zero, as these will cause the function to become undefined. For example, if the function is f(x) = 1/(x-2), the vertical asymptote is x=2.
4. Determine horizontal asymptotes: Horizontal asymptotes occur when the function approaches a constant value (often zero or infinity) as x approaches positive or negative infinity. To find them, evaluate the limit of the function as x approaches positive or negative infinity. For example, if the function is f(x) = (3x^2 + 2x - 1)/(2x^2 + 5x + 3), the horizontal asymptote is y = 3/2.
5. Sketch the asymptotes: On a graph, draw vertical lines at the values where vertical asymptotes occur. Then draw horizontal lines at the heights of the horizontal asymptotes. These lines will serve as the asymptotes for the function.
Regarding the difference between set notation and interval notation:
Set notation: Set notation is used to represent a set of numbers. It uses braces { } to enclose the elements of the set. For example, {1, 2, 3} is a set containing the elements 1, 2, and 3.
Interval notation: Interval notation is used to represent a continuous range of numbers. It uses parentheses () or brackets [] to represent open or closed intervals, respectively. For example, (1, 5) represents all numbers between 1 and 5, excluding 1 and 5.
Here is an example to further illustrate the difference:
Set notation: A set containing all even numbers between -4 and 4 can be represented as {-4, -2, 0, 2, 4}.
Interval notation: The same set can be represented in interval notation as [-4, 4], where the square brackets indicate that -4 and 4 are included in the set. If the endpoints were excluded, the notation would be (-4, 4).
Remember that both notations serve the purpose of representing a collection of numbers, but interval notation is particularly useful when describing continuous ranges.