Equation and relation

A

Asma

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Feb 5, 2015
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Hi everyone

I have a quiz and I am really struggling with these questions.

Can you please explain it for me pleas?

(x+3)^2 + (y-4)^2 =25

why this equation defines a relation?

Give the domain and the range of this relation?
Is this relation a also a function?
 
Asma said:
Hi everyone

I have a quiz and I am really struggling with these questions.

Can you please explain it for me pleas?

(x+3)^2 + (y-4)^2 =25

why this equation defines a relation?

Give the domain and the range of this relation?
Is this relation a also a function?
Click to expand...
This is the equation of a circle. What is the center? Which values can x be (domain)? Which values can y be (range)? If you were to draw this circle then you will be able to see the answer to my last two question. People on this forum will help you but we need to see some input from you as well.
 
Jomo said:
This is the equation of a circle. What is the center? Which values can x be (domain)? Which values can y be (range)? If you were to draw this circle then you will be able to see the answer to my last two question. People on this forum will help you but we need to see some input from you as well.
Click to expand...

Thank you


I have already got the answer but I am not really sure. Also, I was not able to figure out the reason why the equation defines a relation


The center is (-3,4)
Domain =(-8,2)
Range= (-1,9)
 
Asma said:
Thank you


I have already got the answer but I am not really sure. Also, I was not able to figure out the reason why the equation defines a relation


The center is (-3,4)
Domain =(-8,2)
Range= (-1,9)
Click to expand...


A relation is a set of ordered pairs. The equation you've given will be true for a set of pairs of the form (x, y), thus this equation defines a relation. And you've described its graph. In order for a relation to be a FUNCTION, no two of the ordered pairs can have the same first element (and no vertical line can intersect the graph in more than one point.) How about your circle? Is it possible to draw a vertical line which intersects the graph of the circle in more than one point? If that's possible, this relation is NOT a function.
 
Asma said:
Thank you


I have already got the answer but I am not really sure. Also, I was not able to figure out the reason why the equation defines a relation


The center is (-3,4)
Domain =(-8,2)
Range= (-1,9)
Click to expand...
Yes, you are correct. Very good. Here is a nice way to do these type problems.
1) find the center (-3,4)
2) find the radius 5
3) domain is (-3-5, -3 + 5) = (-8, 2)
4) range is (4-5, 4 + 5) = (-1, 9)

Why does the equation define a relation? Because each point on the circle is an ordered pair--(x,y)

Is the equation a function or not?
 
Last edited:
Thank you for both of you

you really helped me a lot

Best Regards
 
Since your difficulty was in determining whether or not the equation gave a relation, did it not occur to you to look up the definition of "relation" in your text book?

Can you now tell why this equation does NOT define a "function"? What is the definition of "function" in your text book.
 
lookagain said:
Jomo, no, that user is not correct. The last two are wrong.

Domain: [-8, 2]

Range: [-1, 9]
Click to expand...
I should have looked again before I submitted my post. In any case I appreciate that you pointed this out to me.
 
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