is the vertical asymptotes in the numerator or denominator? why? can you please explain you answer
vertical asymptotes have slopes which are undefined.
An answer of "undefined" is caused by division of zero.
So what is your conclusion?
Sooo would I write that because vertical asymptotes are undefined whuch is caused by the division of zero, it's in the denominator?
yes
Vertical asymptotes can exist in both the numerator and the denominator, depending on the specific characteristics of the function.
In general, vertical asymptotes occur when the denominator of a rational function becomes zero and the numerator is not zero at that point. This is because division by zero is undefined in mathematics. When the denominator becomes zero, the fraction becomes undefined and the function approaches positive or negative infinity as it gets infinitely close to that point.
The numerator plays a role in determining whether a vertical asymptote exists in the numerator or denominator. If the numerator has a factor that cancels out with the factor in the denominator that causes it to become zero, then the vertical asymptote will be in the numerator. On the other hand, if the numerator does not cancel out with the denominator, then the vertical asymptote will be in the denominator.
To determine if a function has a vertical asymptote in the numerator or denominator, you can analyze the factors of the numerator and denominator separately. Look for any common factors that can cancel out, which would indicate a vertical asymptote in the numerator. If there are no common factors that cancel out, the vertical asymptote will be in the denominator.
Remember that this explanation is applicable to rational functions, where the function is defined as the ratio of two polynomials. Other types of functions may have different characteristics when it comes to determining asymptotes.