Graphing rational functions is a relatively straightforward procedure. The first step is to find the x-intercepts. These are points on the x-axis that are undefined. Then, use this fact to locate the y-intercepts. Then, use this fact to solve for x. For vertical asymptotes, find the y-intercepts.
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Similarly, the first step in solving a linear equation is to find the horizontal asymptote of f(x). A rational function will never reach its y-intercept, but it will approach the vertical asymptote line. It may be horizontal, vertical, or slant. The denominator and numerator must have the same degree in order to determine the asymptote.
If you find the horizontal asymptote, the vertical asymptote is also a horizontal asymptote. Graph the graph to see where the denominator becomes zero. Then, determine where the vertical asymptote intersects the horizontal asymptote. If the line is at a point where the graph crosses the asymptote, the graph has reached the vertical asymptote.
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As the graph approaches the horizontal asymptote, it must approach the y-intercepts of the function. If it does, the graph will be stationary. If it crosses the asymptote, it is considered a linear asymptote. The answer to this question is the slope of the line. Besides being a straight line, the vertical asymptote is a slant line.
The vertical asymptote is the line with the highest degree. Its value is x = -2. The horizontal asymptote crosses the x-intercept. The denominator must be higher than the numerator. If it does, it is a horizontal asymptote. However, it is important to remember that the vertical asymptote does not cross the y-intercept.
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As a graph approaches a vertical asymptote, the horizontal asymptote crosses the horizontal asymptote. The vertical asymptote is the line that reaches a zero-point. The two asymptotes are not the same. The first is the x-value of the horizontal asymptote.
Graphing a horizontal asymptote is a very easy process compared to the vertical asymptote. If y-intercepts are zero, then the horizontal asymptote is y=0. The other two asymptotes are x=0. The other two asymptopes are x=0 and y=b.
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If x-intercepts a line, then x=b. The denominator is b. The horizontal asymptote is the line of x. A vertical asymptote will have a hole, while a horizontal asymptote is a horizontal asymptote.
When graphing a rational function, always consider the x-intercepts. If you are examining the x-intercepts, you must look for the y-intercepts of a rational function. The horizontal asymptote is where a function crosses a line. The vertical asymptote is the same as a horizontal asymptote.
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A horizontal asymptote is the point where the numerator does not cross the y-axis. The horizontal asymptote is the horizontal asymptote. A slant asymptote is a vertical asymptote. The denominator has a constant value. The y-intercept is the y-intercept of the function.
A vertical asymptote occurs when the graph of a function approaches the line that gives it the value x. A horizontal asymptote is where the graph of a vertical asymptote approaches the line of y = 0 and becomes very large. If x is approaching a horizontal asymptote, it is a horizontal asymptote.
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