When it comes to rational functions, there are two ways to find the range depending on if the denominator is a linear expression or if it is a quadratic expression.

Let’s see the steps for each case.

Steps to determining the range of a rational function (denominator is a linear expression):

1. Find the inverse of the function

- Set the function equal to y, and solve for x

2. Find the domain of the inverse

- Substitute
at the end

3. Write the range

- Refer to previous blog post on domains if you need help with this

Steps to determining the range of a rational function (denominator is a quadratic expression):

- The domain of the inverse is the range of the function when you substitute y or
for x

1. Multiply the denominator to both sides of the equation

2. Find the discriminant in terms of y

- Set

3. Set the discriminant greater than or equal to 0 and solve for y

- discriminant=
, given

- Make a table to summarize the results if needed

4. Write the range

- Show when the factors of the discriminant and the discriminant are positive, negative, and 0

Let’s see an example for when the denominator is a linear expression (click here):

- The range is the set of y for which the discriminant is equal to or great than 0

Find the range of

1. Find the inverse of the function

2. Find the domain of the inverse

Domain: or ,or

3. Write the range

Range: or ,or

Now let’s see an example when the denominator is a quadratic expression (click here):

Find the range of

1. Multiply the denominator to both sides of the equation

2. Find the discriminant in terms of y

discriminant=

3. Set the discriminant greater than or equal to 0 and solve for y

4y is 0 when:y=0 y+4 is 0 when:y=-4

4y is negative when:y<0 y+4 is negative when:y<-4

4y is positive when:y>0 y+4 is positive when:y>-4

0 | + | ||||

0 | + | + | + | ||

4. Write the range

, , ,

Range: or , or

We’ll see one more example because it is tricky (click here):

Find the range of

1. Multiply the denominator to both sides of the equation

2. Find the discriminant in terms of y

Discriminant=

3. Set the discriminant greater than or equal to zero and solve for y

or

Note: We did not have to make a table because this was a simpler way to solve for y

4. Write the range

Range: , or

As you can see, finding the range of a function is trickier, especially finding the range of a rational function. It might seem hard and a little scary, but the more practice you get with this, the better you will become. For more help or practice on this topic, visit Symbolab’s Practice.

Until next time,

Leah

This blog is consisting of some formulas and you know that math is very difficult subject. But this subject is really nice and students should to taking interest in this subject but custom thesis writing service is the best option for all. You give the good information and solve this equation.

ReplyDeleteMaths was never my favorite subject and no matter what I do I could never ace in it. This blog has helped me tremendously and I have finally started getting a better understanding of this subject.

ReplyDeleteMaths was never my most loved subject and regardless of what I do I would never pro in it. This blog has helped me colossally and I have at long last begun showing signs of improvement comprehension of this subject. UK Dissertation Help

ReplyDeleteThis comment has been removed by the author.

ReplyDeleteFor a function f defined by an expression with variable x, the implied domain of f is the set of all real numbers variable x can take such that the expression defining the function is real. The domain can also be given explicitly. Dissertation writing

ReplyDeleteToko Online Spesialis Herbal Indonesia menyediakan obat herbal bermutu tinggi dengan tujuan memperbaiki performa kesehatan tubuh. Situs Kesehatan Spesialisherbal merupakan pusat obat herbal yang menjual obat herbal bermutu yang terpercaya di Nusantara.

ReplyDeleteHello.My blog of Math .

ReplyDeleteHello.My blog of Math .

ReplyDeleteI just loved your way of presentation. enjoyed reading this .Thanks for sharing and keep writing. It is Obat Gondok Beracun like this. As constantly, we appreciate yourself assurance and accept as true within us.

ReplyDeleteSitus SBOBET TerpercayaThis post is not just informative but impressive also. The post is so convincing that it created an urge to choose Dissertation Help Services. You can email us at [email protected] or Phone Number: 020 8144 9988.

ReplyDeleteDissertation Writing Services

Pname Com Facebook Orca blunders on Android is a classic problem and many customers have tried to investigate how it may appear and the way they.

ReplyDeleteWhatsApp online status is one of the most widely used instant messaging apps on mobile devices thanks to its low data usage and ability to be used internationally. WhatsApp online status

ReplyDeleteOur declaration to providing the best customer experience when it comes to the term papers for sale online are guided by these principles we entrench daily in our delivery for the delivery of cheap custom essay writing services.

ReplyDelete

ReplyDeletefast social follower will provide you the best social media services such as Buy youtube views , Buy Youtube views cheap , buy targeted youtube views .

Amazing article. Digital Marketing Agency in Lahore

ReplyDeleteThe guideline how to do a case brief can be very helpful for you if you have to write this essay for the first time or if it's not the most easier assignment for you. As an alternative, get the well-wrriten paper by the proficient writers of the prime-essay.net writing service.

ReplyDelete