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Why do functions with vertical asympotes sometimes have a numerator of x and other times numerator of 1?
This is because whether a function has a vertical asymptote (VA) or not is not affected by the numerator. The denominator is where the VA originates when you try to divide by 0. For example, y=x/(x-1) and and y=1/(x-1) BOTH have VAs when the denominator is equal to zero. x-1=0 when x=1, so that's where the VA is, regardless of the numerator.
What else can I help you with?
How do you tell if a function with a vertical asympote has a numerator of 1 or a numerator of x?
If there are no coordinates given then you cannot.
Do all rational functions have holes?
Not all rational functions have holes. A rational function is a ratio of two polynomials, and holes occur at points where both the numerator and denominator equal zero, indicating a common factor. If a rational function has no common factors between the numerator and denominator, it will not have any holes, although it may have vertical asymptotes or other features.
How do you solve asymptote?
To solve for asymptotes of a function, you typically look for vertical, horizontal, and oblique asymptotes. Vertical asymptotes occur where the function approaches infinity, typically at values where the denominator of a rational function is zero but the numerator is not. Horizontal asymptotes are determined by analyzing the behavior of the function as it approaches infinity; for rational functions, this involves comparing the degrees of the polynomial in the numerator and denominator. Oblique asymptotes occur when the degree of the numerator is one higher than that of the denominator, and can be found using polynomial long division.
Do all lines represent functions?
No. Vertical lines are not.
Are vertical angles alway sometimes or never supplementary?
sometimes
How do you tell if a function with a vertical asympote has a numerator of 1 or a numerator of x?
If there are no coordinates given then you cannot.
Do all rational functions have holes?
Not all rational functions have holes. A rational function is a ratio of two polynomials, and holes occur at points where both the numerator and denominator equal zero, indicating a common factor. If a rational function has no common factors between the numerator and denominator, it will not have any holes, although it may have vertical asymptotes or other features.
What is the vertical line called separating the numerator from the denominator?
It's called a vinculum.
How do you solve asymptote?
To solve for asymptotes of a function, you typically look for vertical, horizontal, and oblique asymptotes. Vertical asymptotes occur where the function approaches infinity, typically at values where the denominator of a rational function is zero but the numerator is not. Horizontal asymptotes are determined by analyzing the behavior of the function as it approaches infinity; for rational functions, this involves comparing the degrees of the polynomial in the numerator and denominator. Oblique asymptotes occur when the degree of the numerator is one higher than that of the denominator, and can be found using polynomial long division.
Are all functions linear?
yes yes No, vertical lines are not functions
Are all equations functions?
yes yes No, vertical lines are not functions
Are all linear equations functions?
yes yes No, vertical lines are not functions
Do all lines represent functions?
No. Vertical lines are not.
Vertical angles are always sometimes or never complimentary?
Sometimes
Are vertical angles alway sometimes or never supplementary?
sometimes
Why are soil layers sometimes vertical?
== ==
Why does your computer screen have vertical lines on it sometimes?
If your computer screen has vertical lines on it sometimes your monitor or graphics card may be dying.
