Finding Asymptotes - Math
Card 1 of 8
A function is defined by the following rational equation:
What are the horizontal and vertical asymptotes of this function's graph?
A function is defined by the following rational equation:
What are the horizontal and vertical asymptotes of this function's graph?
Tap to reveal answer
To find the horizontal asymptote, compare the degrees of the top and bottom polynomials. In this case, the two degrees are the same (1), which means that the equation of the horizontal asymptote is equal to the ratio of the leading coefficients (top : bottom). Since the numerator's leading coefficient is 1, and the denominator's leading coefficient is 2, the equation of the horizontal asymptote is 
.
To find the vertical asymptote, set the denominator equal to zero to find when the entire function is undefined:
To find the horizontal asymptote, compare the degrees of the top and bottom polynomials. In this case, the two degrees are the same (1), which means that the equation of the horizontal asymptote is equal to the ratio of the leading coefficients (top : bottom). Since the numerator's leading coefficient is 1, and the denominator's leading coefficient is 2, the equation of the horizontal asymptote is
To find the vertical asymptote, set the denominator equal to zero to find when the entire function is undefined:
← Didn't Know|Knew It →
A function is defined by the following rational equation:
What line does 
approach as 
approaches infinity?
A function is defined by the following rational equation:
What line does
Tap to reveal answer
This question is asking for the equation's slant asymptote. To find the slant asymptote, divide the numerator by the denominator. Long division gives us the following:
However, because we are considering 
as it approaches infinity, the effect that the last term has on the overall linear equation quickly becomes negligible (tends to zero). Thus, it can be ignored.
This question is asking for the equation's slant asymptote. To find the slant asymptote, divide the numerator by the denominator. Long division gives us the following:
However, because we are considering
← Didn't Know|Knew It →
A function is defined by the following rational equation:
What are the horizontal and vertical asymptotes of this function's graph?
A function is defined by the following rational equation:
What are the horizontal and vertical asymptotes of this function's graph?
Tap to reveal answer
To find the horizontal asymptote, compare the degrees of the top and bottom polynomials. In this case, the two degrees are the same (1), which means that the equation of the horizontal asymptote is equal to the ratio of the leading coefficients (top : bottom). Since the numerator's leading coefficient is 1, and the denominator's leading coefficient is 2, the equation of the horizontal asymptote is .
To find the vertical asymptote, set the denominator equal to zero to find when the entire function is undefined:
To find the horizontal asymptote, compare the degrees of the top and bottom polynomials. In this case, the two degrees are the same (1), which means that the equation of the horizontal asymptote is equal to the ratio of the leading coefficients (top : bottom). Since the numerator's leading coefficient is 1, and the denominator's leading coefficient is 2, the equation of the horizontal asymptote is
To find the vertical asymptote, set the denominator equal to zero to find when the entire function is undefined:
← Didn't Know|Knew It →
A function is defined by the following rational equation:
What line does approach as approaches infinity?
A function is defined by the following rational equation:
What line does
Tap to reveal answer
This question is asking for the equation's slant asymptote. To find the slant asymptote, divide the numerator by the denominator. Long division gives us the following:
However, because we are considering as it approaches infinity, the effect that the last term has on the overall linear equation quickly becomes negligible (tends to zero). Thus, it can be ignored.
This question is asking for the equation's slant asymptote. To find the slant asymptote, divide the numerator by the denominator. Long division gives us the following:
However, because we are considering
← Didn't Know|Knew It →
A function is defined by the following rational equation:
What are the horizontal and vertical asymptotes of this function's graph?
A function is defined by the following rational equation:
What are the horizontal and vertical asymptotes of this function's graph?
Tap to reveal answer
To find the horizontal asymptote, compare the degrees of the top and bottom polynomials. In this case, the two degrees are the same (1), which means that the equation of the horizontal asymptote is equal to the ratio of the leading coefficients (top : bottom). Since the numerator's leading coefficient is 1, and the denominator's leading coefficient is 2, the equation of the horizontal asymptote is .
To find the vertical asymptote, set the denominator equal to zero to find when the entire function is undefined:
To find the horizontal asymptote, compare the degrees of the top and bottom polynomials. In this case, the two degrees are the same (1), which means that the equation of the horizontal asymptote is equal to the ratio of the leading coefficients (top : bottom). Since the numerator's leading coefficient is 1, and the denominator's leading coefficient is 2, the equation of the horizontal asymptote is
To find the vertical asymptote, set the denominator equal to zero to find when the entire function is undefined:
← Didn't Know|Knew It →
A function is defined by the following rational equation:
What line does approach as approaches infinity?
A function is defined by the following rational equation:
What line does
Tap to reveal answer
This question is asking for the equation's slant asymptote. To find the slant asymptote, divide the numerator by the denominator. Long division gives us the following:
However, because we are considering as it approaches infinity, the effect that the last term has on the overall linear equation quickly becomes negligible (tends to zero). Thus, it can be ignored.
This question is asking for the equation's slant asymptote. To find the slant asymptote, divide the numerator by the denominator. Long division gives us the following:
However, because we are considering
← Didn't Know|Knew It →
A function is defined by the following rational equation:
What are the horizontal and vertical asymptotes of this function's graph?
A function is defined by the following rational equation:
What are the horizontal and vertical asymptotes of this function's graph?
Tap to reveal answer
To find the horizontal asymptote, compare the degrees of the top and bottom polynomials. In this case, the two degrees are the same (1), which means that the equation of the horizontal asymptote is equal to the ratio of the leading coefficients (top : bottom). Since the numerator's leading coefficient is 1, and the denominator's leading coefficient is 2, the equation of the horizontal asymptote is .
To find the vertical asymptote, set the denominator equal to zero to find when the entire function is undefined:
To find the horizontal asymptote, compare the degrees of the top and bottom polynomials. In this case, the two degrees are the same (1), which means that the equation of the horizontal asymptote is equal to the ratio of the leading coefficients (top : bottom). Since the numerator's leading coefficient is 1, and the denominator's leading coefficient is 2, the equation of the horizontal asymptote is
To find the vertical asymptote, set the denominator equal to zero to find when the entire function is undefined:
← Didn't Know|Knew It →
A function is defined by the following rational equation:
What line does approach as approaches infinity?
A function is defined by the following rational equation:
What line does
Tap to reveal answer
This question is asking for the equation's slant asymptote. To find the slant asymptote, divide the numerator by the denominator. Long division gives us the following:
However, because we are considering as it approaches infinity, the effect that the last term has on the overall linear equation quickly becomes negligible (tends to zero). Thus, it can be ignored.
This question is asking for the equation's slant asymptote. To find the slant asymptote, divide the numerator by the denominator. Long division gives us the following:
However, because we are considering
← Didn't Know|Knew It →