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Factoring is usually helpful in identifying zeros of denominators.
If there are not common factors in the numerator and the denominator, the lines x equal the zeros of the denominator are the vertical asymptotes for the graph of the rational function.
Example:
f(x) = x/(x^2 - 1)
f(x) = x/[(x + 1)(x - 1)]
x + 1 = 0 or x - 1 = 0
x = -1 or x = 1
Thus, the lines x = -1 and x = 1 are the vertical asymptotes of f.
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How many non-verticle asymptotes can a rational function have?
Not sure what non-verticle means, but a rational function can have up to 2 non-vertical asymptotes,
How many asymptotes can a bounded function have?
I believe the maximum would be two - one when the independent variable tends toward minus infinity, and one when it tends toward plus infinity. Unbounded functions can have lots of asymptotes; for example the periodic tangent function.
How many asymptotes does a hyperbola have?
A hyperbola has 2 asymptotes.www.2dcurves.com/conicsection/​conicsectionh.html
What slope does a vertical line have?
In terms of the slope intercept form of the line, it is undefined. A vertical line is not a function since a single value of x is mapped onto infinitely many y values.
Is the set of rational numbers finite?
No; there are infinitely many rational numbers.
How many non-verticle asymptotes can a rational function have?
Not sure what non-verticle means, but a rational function can have up to 2 non-vertical asymptotes,
How many vertical asymptotes does the graph of this function have?
2
Can the graph of a rational function have more than one vertical asymptote?
Assume the rational function is in its simplest form (if not, simplify it). If the denominator is a quadratic or of a higher power then it can have more than one roots and each one of these roots will result in a vertical asymptote. So, the graph of a rational function will have as many vertical asymptotes as there are distinct roots in its denominator.
How many asymptotes can a bounded function have?
I believe the maximum would be two - one when the independent variable tends toward minus infinity, and one when it tends toward plus infinity. Unbounded functions can have lots of asymptotes; for example the periodic tangent function.
Limits in calculus?
A limit in calculus is a value which a function, f(x), approaches at particular value of x. They can be used to find asymptotes, or boundaries, of a function or to find where a graph is going in ambiguous areas such as asymptotes, discontinuities, or at infinity. There are many different ways to find a limit, all depending on the particular function. If the function exists and is continuous at the value of x, then the corresponding y value, or f (x), is the limit at that value of x. However, if the function does not exist at that value of x, as happens in some trigonometric and rational functions, a number of calculus "tricks" can be applied: such as L'Hopital's Rule or cancelling out a common factor.
Which function has no horizontal asymptote?
Many functions actually don't have these asymptotes. For example, every polynomial function of degree at least 1 has no horizontal asymptotes. Instead of leveling off, the y-values simply increase or decrease without bound as x heads further to the left or to the right.
How many asymptotes does a ellipse have?
None.
Sketch a Tangent Functions?
A tangent function is a trigonometric function that describes the ratio of the side opposite a given angle in a right triangle to the side adjacent to that angle. In other words, it describes the slope of a line tangent to a point on a unit circle. The graph of a tangent function is a periodic wave that oscillates between positive and negative values. To sketch a tangent function, we can start by plotting points on a coordinate plane. The x-axis represents the angle in radians, and the y-axis represents the value of the tangent function. The period of the function is 2π radians, so we can plot points every 2π units on the x-axis. The graph of the tangent function is asymptotic to the x-axis. It oscillates between positive and negative values, crossing the x-axis at π/2 and 3π/2 radians. The graph reaches its maximum value of 1 at π/4 and 7π/4 radians, and its minimum value of -1 at 3π/4 and 5π/4 radians. In summary, the graph of the tangent function is a wave that oscillates between positive and negative values, crossing the x-axis at π/2 and 3π/2 radians, with a period of 2π radians.
What is vertical line test in a function?
If, at any time, a vertical line intersects the graph of a relationship (or mapping) more than once, the relationship is not a function. (It is a one-to-many mapping and so cannot be a function.)
How many asymptotes does a hyperbola have?
A hyperbola has 2 asymptotes.www.2dcurves.com/conicsection/​conicsectionh.html
What is the graph combination of line segments that passes the vertical line test?
Many to one function
What slope does a vertical line have?
In terms of the slope intercept form of the line, it is undefined. A vertical line is not a function since a single value of x is mapped onto infinitely many y values.
