Give the range of the rational functions given that neither of the graphs crosses its horizontal asymptote. Write your answers in set notation and int

sagnuhh

sagnuhh

Answered question

2021-06-27

Give the range of the rational functions given that neither of the graphs crosses its horizontal asymptote. Write your answers in set notation and interval notation.

Answer & Explanation

Nathanael Webber

Nathanael Webber

Skilled2021-06-28Added 117 answers

1. All real numbers are included in a rational function's range, with the exception of the y values that represent holes or horizontal asymptotes.
In Example B, part(b), the horizontal asymptote was y=2. Therefore, the range is all real numbers, except y=2
The set notation for the range is {yRyq2}
The interval notation is y(,2)(2,)
2. In ‘Try These B, part(a), we were given
y=2xx+4
In a rational function, the horizontal asymptote is determined by if the degree of the numerator and the denominator are equal.
y= (ratio of the leading coefficients in the numerator/denominator)
In this case, we have
y=11=1
Therefore, the set notation for the range is ¢y¢R|y1
The interval notation is y(,1)(1,)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?