Can horizontal asymptote intersect the graph?
The graph of f can intersect its horizontal asymptote. As x → ± ∞, f(x) → y = ax + b, a ≠ 0 or The graph of f can intersect its horizontal asymptote.
Can the graph of a rational function can never cross one of its asymptotes?
A graph CAN cross slant and horizontal asymptotes (sometimes more than once). It's those vertical asymptote critters that a graph cannot cross. This is because these are the bad spots in the domain.
Can a rational function never intersect a vertical asymptote?
Answer and Explanation: A function cannot cross a vertical asymptote, these asymptotes are defined on the values that do not belong to the domain. Horizontal asymptotes are imaginary horizontal lines that the function can cross.
Can a graph intersect a vertical asymptote?
It is impossible for the graph of a function to intersect a vertical asymptote (or a vertical line in general) in more than one point. Moreover, if a function is continuous at each point where it is defined, it is impossible that its graph does intersect any vertical asymptote.
How do you know if a rational function crosses the horizontal asymptote?
6) Determine if the graph will intersect its horizontal or slant asymptote. a. If there is a horizontal asymptote, say y=p, then set the rational function equal to p and solve for x. If x is a real number, then the line crosses the horizontal asymptote at (x,p).
Why can horizontal asymptotes be crossed?
As we look at the function going in the x direction, the function can cross its horizontal asymptote as long as it can turn back around and tend towards it at infinity. To put it another way, the function can cross this horizontal asymptote as long as you are not beyond all of the possible turning points.
Which asymptote direction can a function not cross?
A function cannot cross a vertical asymptote because the graph must approach infinity (or −∞) from at least one direction as x approaches the vertical asymptote. However, a function may cross a horizontal asymptote.
What is a horizontal asymptote?
A horizontal asymptote of a graph is a horizontal line y = b where the graph approaches the line as the inputs approach ∞ or –∞. A slant asymptote of a graph is a slanted line y = mx + b where the graph approaches the line as the inputs approach ∞ or –∞.
Why can't a rational function have both a horizontal and an oblique asymptote?
If there is a horizontal asymptote, then the behavior at infinity is that the function is getting ever closer to a certain constant. If there is an oblique asymptote, then the function is getting ever closer to a line which is going to infinity. A function can't go to a finite constant and infinity at the same time.
Can a graph intersect an oblique asymptote?
Note that your graph can cross over a horizontal or oblique asymptote, but it can NEVER cross over a vertical asymptote.
What is a vertical and horizontal asymptote?
Vertical asymptotes mark places where the function has no domain. You solve for the equation of the vertical asymptotes by setting the denominator of the fraction equal to zero. Horizontal asymptotes, on the other hand, indicate what happens to the curve as the x-values get very large or very small.
What is a vertical asymptote?
A vertical asymptote is a vertical line that guides the graph of the function but is not part of it. It can never be crossed by the graph because it occurs at the x-value that is not in the domain of the function.
Which asymptote direction can a function not cross?
A function cannot cross a vertical asymptote because the graph must approach infinity (or −∞) from at least one direction as x approaches the vertical asymptote. However, a function may cross a horizontal asymptote.
Can a rational function intersect a horizontal asymptote?
Expert Answer. 1: True, the graph of a rational function can cross a horizontal Asymptote.
Can there be more than one vertical asymptote?
VERTICAL ASYMPTOTES, x = c A vertical asymptote is a vertical line that guides the graph of the function but is not part of it. It can never be crossed by the graph because it occurs at the x-value that is not in the domain of the function. A function may have more than one vertical asymptote.
Does every rational function have a vertical asymptote?
Not all rational functions will have vertical asymptotes. Algebraically, for a rational function to have a vertical asymptote, the denominator must be able to be set to zero while the numerator remains a non-zero value.
Problem 3 Medium Difficulty
Which type of asymptote will never intersect the graph of a rational function? (a) horizontal (b) oblique (d) all of these (c) vertical
Video Transcript
problem. Three of section 5.3 asked to determine which of the listed Assam totes cannot be cross. So we're going to start by looking at this equation that I've right now on the right. And, um, we're going to try and prove these things on the list, which can or cannot be crossed.