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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.
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 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.
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.
An asymptote is a line that the graph of a function?
approaches but does not cross
What is the equation of the asymptote of the graph of?
To determine the equation of the asymptote of a graph, you typically need to analyze the function's behavior as it approaches certain values (often infinity) or points of discontinuity. For rational functions, vertical asymptotes occur where the denominator equals zero, while horizontal asymptotes can be found by comparing the degrees of the numerator and denominator. If you provide a specific function, I can give you its asymptote equations.
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.
Given the rational function 2x-3x2 -5x-6 find the verticle and horizontal asymptotes?
f(x) = (2x - 3x2)/(-5x - 6)f(x) = -(3x2 - 2x)/-(5x + 6)f(x) = (3x2 - 2x)/(5x + 6)5x + 6 = 05x + 6 - 6 = 0 - 65x = -65x/5 = -6/5x = -6/5 (the vertical asymptote of f)Since the degree of the polynomial function in the numerator is greater than the degree of the polynomial function in the denominator, then the graph of f has no horizontal 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.
Can a slant asymptote cuts the graph?
No. If it cuts a graph it is not an asymptote.
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.
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
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
