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Can a slant asymptote cuts the graph?
No. If it cuts a graph it is not an asymptote.
Name the functions whose graph looks like a set of stairs?
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
What will be graph if an asymptote of it touches at three points?
if it touches at three points it is a straight line. Since it is also an asymptote, it will be a straight horizontal line (zero slope)
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.
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.
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.
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.
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
How do you find the horizontal asymptote in a graph of a rational function?
The horizontal asymptote is what happens when x really large. To start with get rid of all the variables except the ones with the biggest exponents. When x is really large, they are the only ones that will matter. If the remaining exponents are the same, then the ratio of those coefficients tell you where the horizontal asymptote is. For example if you have 2x3/3x3, then the ratio is 2/3 and the asymptote is f(x)=2/3 or y=2/3. If the exponent in the denominator is bigger, than y=0 is the horizontal asymptote. If the exponent in the numerator is bigger, than there is no horizontal asymptote.
Name the functions whose graph looks like a set of stairs?
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
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.
