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This gives practice for finding horizontal asymptotes of rational functions.
How You Can (And Should) Get More Practice!
Below is a few practice problems of various difficulty, but you will need considerably more practice than one each. For that reason
you should definitely use the green “Try Another” button in the top right corner at least two or three times to complete
additional versions of these questions for more practice. You should keep using that button until doing these problems feels straight
forward and easy, and then come back after a week or so of doing other stuff and try again to make sure it is still just as easy for
you.
Theoretically Easier Difficulty Problem
To compute a horizontal asymptote for a rational function with polynomials for denominator and numerator, start by checking
the degree of both the numerator and denominator polynomials.
If the degree in the numerator is higher than the degree in the denominator, then there is no HA. If the degree is the same, then the HA is the ratio of the leading coefficients (i.e. the leading coefficient of the numerator divided by
the leading coefficient of the denominator) If the degree of the denominator is larger than the degree of the numerator, then the HA is zero.
Consider the function: has a horizontal asymptote of: (If there is no horizontal asymptote, enter ’DNE’)
Theoretically Medium Difficulty Problem
To compute a horizontal asymptote for a rational function with polynomials for denominator and numerator, start by checking
the degree of both the numerator and denominator polynomials.
If the degree in the numerator is higher than the degree in the denominator, then there is no HA. If the degree is the same, then the HA is the ratio of the leading coefficients (i.e. the leading coefficient of the numerator divided by
the leading coefficient of the denominator) If the degree of the denominator is larger than the degree of the numerator, then the HA is zero.
Consider the function: has a horizontal asymptote of: (If there is no horizontal asymptote, enter ’DNE’)
Theoretically Harder Difficulty Problem
To compute a horizontal asymptote for a rational function with polynomials for denominator and numerator, start by checking
the degree of both the numerator and denominator polynomials.
If the degree in the numerator is higher than the degree in the denominator, then there is no HA. If the degree is the same, then the HA is the ratio of the leading coefficients (i.e. the leading coefficient of the numerator divided by
the leading coefficient of the denominator) If the degree of the denominator is larger than the degree of the numerator, then the HA is zero.
Consider the function: if has , then which of the following is a possible degree of the polynomial ?
