anonymous one year ago Need help with assignment on graphing rational functions and domain and range. I do not understand the concept! This is what I have to do. - Assignment: Graph the functions and describe the domain and range of each function. (Will post screenshot of 5 equations in attachments below.) The help would be so appreciated. Will award medal of course

1. anonymous

2. anonymous

i would suggest going to desmos.com and use there graphing calculator. It is perfect for what you need and i have had similar equations.

3. anonymous
4. anonymous

However i can try to explain it but it would not be the best.

5. anonymous

for the first equation type into desmos f(x) = 1/(x + 1)

6. anonymous

I will try that now. I like also that it shows the graph. As part of the assignment I have to explain/state the domain/ range of each function. Do you know how to do that?

7. anonymous

basically they want you to say something along the lines of "the domain is all real numbers because blah blah blah" and the same thing for the range. You do know what range and domain means right? domain is x and range is y

8. anonymous

I do know that definition. However, I do not know much more than that, and consequently I do not know how to determine the domain/range of any of the 5 equations.

9. anonymous

@triciaal i cant help him any further explaining this.

10. anonymous

I Myself have a hard time understanding this...... i would suggest googling how to explain the domain and range of a function... unfortunately that is all the advice i can give...

11. anonymous

ok!! I understand. I am confused as well. Haha thanks

12. pooja195

See if this helpes with the describing aspect :) http://www.purplemath.com/modules/fcns2.htm

13. anonymous

thank you!!

14. UsukiDoll

The domain is in the x-axis and the range is in the y axis... it helps to graph the equation and use that information to analyze it. So, I'll do one as an example. $f(x) = \frac{1}{x+1}$ Since we have a fraction, that means that there is a restriction. The restriction occurs when x is a certain number that causes this fraction to become undefined so we solve for x+1=0 and that's x = -1.

15. UsukiDoll

so at x = -1 there should be nothing. It's a break.

16. UsukiDoll

so for the domain it's all real numbers except when x = -1

17. UsukiDoll

now the range is a bit trickier than the domain because we need to focus on the y-axis. Assuming that the graph covers all y values, then the range will be all real numbers.

18. anonymous

Hey so there are a few ways to do this. I don't know how much you know about these functions but lets start fresh. We'll do the first one and see if you understand it and then we can move on to the rest. $f(x) = \frac{ 1 }{ x+1 }$ I don't know if you've learned transformations at this point, but usually when we have f(x), it's the same thing as y, so we can say y = f(x) so it is more clear. So lets treat this function as $y= \frac{ 1 }{ x+1 }$ I think a good way to do this is by knowing the basic functions and then transforming it into what already exists, so the basic function here is, $f(x) = \frac{ 1 }{ x } ~~~ or ~~~y = \frac{ 1 }{ x }$ so if we make a table and plot the points for it we would get a shape called "asymptote" as it never hits 0, if you would like me to make the table please ask but the shape should look as such, |dw:1437634115188:dw| this is the basic function we are dealing with, and then to graph the $y = \frac{ 1 }{ x+1 }$ "x+1" part you would give a horizontal shift to the left |dw:1437634200779:dw| notice how it was shifted to the left side of the graph, you can also confirm this by making a table of values. To find the domain we look at the denominator (where the x is, as domain is deals with the restrictions of the x values) and set it up as such $x+1 \neq 0$ solving for x we get $x \neq -1$ so our domain is all real numbers except for x cannot equal to -1. Now the range deals with the y values, what y values would work/ restrict it. Note the restriction for y values is y cannot be 0 as you can see by the graph it will never touch it. So if you want to put it in mathematical notation we can say the domain is as the following |dw:1437634822460:dw| if you don't understand something don't worry too much, just ask, it takes time to get used to these things. This may seem like a hefty example as well but when you start doing it, you will get the hang of it and do it very quickly. I hope that helps!

19. anonymous

|dw:1437635358343:dw|

20. UsukiDoll

dang... forgot about y can't equal to 0.. it has something to do with that blank. so range is all real numbers except x can't equal to 0