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Jan Hill
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Homework Statement
would there be a horizontal asymptote for y= 6/x - 3
Homework Equations
I know that the vertical asymptote is x =3 because there the expression is undefined
Yes, there is a horizontal asymptote. Any rational function in which the degree of the numerator is equal to the degree of the denominator or the degree of the numerator is less than that of the denominator always has a horizontal asymptote.Jan Hill said:Homework Statement
would there be a horizontal asymptote for y= 6/x - 3
Homework Equations
I know that the vertical asymptote is x =3 because there the expression is undefined
A horizontal asymptote is a line that a graph approaches but never touches as the x or y values become infinitely large or small.
To find the horizontal asymptote of a function, you can look at the highest degree in the numerator and denominator of the function. If the degrees are the same, the horizontal asymptote is the ratio of the leading coefficients. If the degree of the denominator is greater, there is no horizontal asymptote. If the degree of the numerator is greater, the horizontal asymptote is y = 0.
No, not all functions have a horizontal asymptote. Some functions have a slant asymptote, where the graph approaches a line at a specific angle. Other functions have no asymptote at all.
Yes, a function can have more than one horizontal asymptote. This can occur when the degrees in the numerator and denominator are the same, but the leading coefficients are different. In this case, there will be a horizontal asymptote for each ratio of the leading coefficients.
If a function crosses its horizontal asymptote, it means that the graph intersects the asymptote at least once. To determine if this occurs, you can set the function equal to the horizontal asymptote and solve for x. If there is a solution, then the graph crosses the asymptote. If there is no solution, then the graph does not cross the asymptote.