What is the relationship between asymptotes and domain and range?

Or Y<=10. So you don’t get a full range of values out of the equation. Example 3. Domain is the x numbers that you can put in the equation that work.

Do slant asymptotes affect the domain?

The domain would be all real numbers; \begin{align*}x \ne -5\end{align*}. Because of the slant asymptote, there are no restrictions on the range. Because the degree of the numerator is less than the degree of the denominator, there will be a horizontal asymptote along the \begin{align*}x\end{align*}-axis.

What is the domain if there is no vertical asymptote?

Since the denominator has no zeroes, then there are no vertical asymptotes and the domain is “all x”. Since the degree is greater in the denominator than in the numerator, the y-values will be dragged down to the x-axis and the horizontal asymptote is therefore “y = 0”.

Can you have two different values for each domain Why or why not?

Hence, every given domain value has one and only one range value as a result, but not necessarily vice versa. In other words, two different values of x can have the same y -value, but each y -value must be joined with a distinct x -value.

Why does asymptote exist?

An asymptote is a line that a graph approaches without touching. Similarly, horizontal asymptotes occur because y can come close to a value, but can never equal that value. In the previous graph, there is no value of x for which y = 0 ( ≠ 0), but as x gets very large or very small, y comes close to 0.

What is the relationship between the range and horizontal asymptote?

If the degree of the polynomial in the numerator is less than that of the denominator, then the horizontal asymptote is the x -axis or y=0 . The function f(x)=ax,a≠0 has the same domain, range and asymptotes as f(x)=1x .

How do you know if there is an asymptote?

The horizontal asymptote of a rational function can be determined by looking at the degrees of the numerator and denominator.

1. Degree of numerator is less than degree of denominator: horizontal asymptote at y = 0.
2. Degree of numerator is greater than degree of denominator by one: no horizontal asymptote; slant asymptote.