0
To get a good idea of how its graph should look should you check the value of a function on its asymptote?
Wiki User
∙ 13y ago
FALSE
Wiki User
∙ 13y ago
Add your answer:
Earn +20 pts
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
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
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.
What is a line that a graph gets closer and closer to but does not touch?
Asymptote
Should you check the value of a function on its asymptote to get a good idea of how its graph should look?
The asymptote is a line where the function is not valid - i.e the function does not cross this line, in fact it does not even reach this line, so you cannot check the value of the function on it's asymptote.However, to get an idea of the function you should look at it's behavior as it approaches each side of the asymptote.
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
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.
By checking the values for a function on only one side of its asymptote you can know for sure how the graph should look?
false
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
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.
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.
Why is it okay for a graph to cross one of its's horizontal asymptotes?
There is nothing in the definition of "asymptote" that forbids a graph to cross its asymptote. The only requirement for a line to be an asymptote is that if one of the coordinates gets larger and larger, the graph gets closer and closer to the asymptote. The "closer and closer" part is defined via limits.
