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Can the graph of a rational function have more than one vertical asymptote?
Wiki User
∙ 13y ago
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.
Wiki User
∙ 13y ago
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Can the graph of a polynomial function have a vertical asymptote?
no
An asymptote is a line that the graph of a function?
approaches but does not cross
What is A line that a graph approaches but does not reach It may be a vertical horizontal or slanted line?
It is an asymptote.
A line is an for a function if the graph of the function gets closer and closer to touching the line but never reaches it?
asymptote
How can you tell if a graph sHow is a function?
Test it by the vertical line test. That is, if a vertical line passes through the two points of the graph, this graph is not the graph of a function.
Why doesnt the graph of a rational function cross its vertical asymptote?
It can.
Can the graph of a polynomial function have a vertical asymptote?
no
Can the graph of a function have a point on a vertical asymptote?
No. The fact that it is an asymptote implies that the value is never attained. The graph can me made to go as close as you like to the asymptote but it can ever ever take the asymptotic value.
Does every rational function have a vertical asymptote?
Answer: no [but open to debate] ((x-1)(x-2)(x+2))/(x-3) (x^2-3x+2)/(x-2)(x+2) Asymptote missing, graph it, there is no Asymptote because the (x-2)(x+2) can be factored out. yes
Can the graph of a rational function have both a horizontal and oblique asymptote?
Piece wise functions can do everything. Take two pieces of two rational functions, one have a horizontal asymptote as x goes to -infinity and the other have a slanted (oblique) one as x goes to +infinity. It is still a rational function.
An asymptote is a line that the graph of a function?
approaches but does not cross
What is A line that a graph approaches but does not reach It may be a vertical horizontal or slanted line?
It is an asymptote.
What is the term for A line that a graph approaches but does not reach It may be a vertical horizontal or slanted line?
An asymptote.
What is a rational function graph?
The Equation of a Rational Function has the Form,... f(x) = g(x)/h(x) where h(x) is not equal to zero. We will use a given Rational Function as an Example to graph showing the Vertical and Horizontal Asymptotes, and also the Hole in the Graph of that Function, if they exist. Let the Rational Function be,... f(x) = (x-2)/(x² - 5x + 6). f(x) = (x-2)/[(x-2)(x-3)]. Now if the Denominator (x-2)(x-3) = 0, then the Rational function will be Undefined, that is, the case of Division by Zero (0). So, in the Rational Function f(x) = (x-2)/[(x-2)(x-3)], we see that at x=2 or x=3, the Denominator is equal to Zero (0). But at x=3, we notice that the Numerator is equal to ( 1 ), that is, f(3) = 1/0, hence a Vertical Asymptote at x = 3. But at x=2, we have f(2) = 0/0, 'meaningless'. There is a Hole in the Graph at x = 2.
The horizontal asymptote for exponential function is?
The graph of an exponential function f(x) = bx approaches, but does not cross the x-axis. The x-axis is a horizontal asymptote.
Can a slant asymptote cuts the graph?
No. If it cuts a graph it is not an asymptote.
A line is an for a function if the graph of the function gets closer and closer to touching the line but never reaches it?
asymptote
