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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 polynomial function have a vertical asymptote?
no
What is a line that a graph gets closer and closer to but does not touch?
Asymptote
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 a line that a graph gets increasingly closer to but never touches?
A line that a graph gets increasingly closer to but never touches is known as an asymptote. Asymptotes can be horizontal, vertical, or oblique, depending on the behavior of the graph as it approaches infinity or a particular point. For example, the horizontal line (y = 0) serves as an asymptote for the function (y = \frac{1}{x}) as (x) approaches infinity.
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
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
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.
What is a line that a graph gets closer and closer to but does not touch?
Asymptote
Asymptote?
a line that a graph approaches as you move away from the origin
Can a slant asymptote cuts the graph?
No. If it cuts a graph it is not an asymptote.
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.
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.
What is a line that a graph gets increasingly closer to but never touches?
A line that a graph gets increasingly closer to but never touches is known as an asymptote. Asymptotes can be horizontal, vertical, or oblique, depending on the behavior of the graph as it approaches infinity or a particular point. For example, the horizontal line (y = 0) serves as an asymptote for the function (y = \frac{1}{x}) as (x) approaches infinity.
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.
