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Why is the denominator set to zero to graph a rational expression?
When the denominator is equal to zero, the expression is undefined. Close to those places, the expression tends towards plus infinity, or minus infinity. In other words, setting the denominator to zero will tell you where there are vertical asymptotes.
What do the asymptotes represent when you graph the tangent function?
When you graph a tangent function, the asymptotes represent x values 90 and 270.
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,
Can a rational function have no vertical horizontal oblique asymptotes?
No, it will always have one.
What happens in the graphs of the functions that have variables in the denominator?
The answer depends on the form of the expression in the denominator. For example, the graph os 1/(1 + x2) has a pretty well-behaved graph, with a maximum vaue of 1 when x = 0 and asymptotes of y = 0
Why is the denominator set to zero to graph a rational expression?
When the denominator is equal to zero, the expression is undefined. Close to those places, the expression tends towards plus infinity, or minus infinity. In other words, setting the denominator to zero will tell you where there are vertical asymptotes.
What do the asymptotes represent when you graph the tangent function?
When you graph a tangent function, the asymptotes represent x values 90 and 270.
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
What are the equation of the asymptotes for each graph?
that's simple an equation is settled of asymptotes so if you know the asymptotes... etc etc Need more help? write it
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.
Can a rational function have no vertical horizontal oblique asymptotes?
No, it will always have one.
Why are asymptotes important characteristics of rational functions?
Asymptotes are one way - not the only way, but one of several - to analyze the general behavior of a function.
What happens in the graphs of the functions that have variables in the denominator?
The answer depends on the form of the expression in the denominator. For example, the graph os 1/(1 + x2) has a pretty well-behaved graph, with a maximum vaue of 1 when x = 0 and asymptotes of y = 0
How many vertical asymptotes can there be in a rational function?
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.
Is it possible for graph of function to cross the horizontal assymptotes?
When you plot a function with asymptotes, you know that the graph cannot cross the asymptotes, because the function cannot be valid at the asymptote. (Since that is the point of having an asymptotes - it is a "disconnect" where the function is not valid - e.g when dividing by zero or something equally strange would occur). So if you graph is crossing an asymptote at any point, something's gone wrong.
A rational expression minus another rational expression is?
Another rational expression.
