anonymous
  • anonymous
Which of the following expressions represents a function? A. x=1 B. {(3,2), (3, -2), (4, 5), (4,-5)} C. y= 4x-1 D.4x^2+y^2=16
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Please help, I'm stuck!
anonymous
  • anonymous
In order for the expression to be a function, there must exist, for each value in the domain i.e. every x-value, one and only one value in the range i.e. y-value. Which one do you think it is?
jdoe0001
  • jdoe0001
how can you tell a function from just a relation? hint: recall your DOMAIN and RANGE sets

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anonymous
  • anonymous
Ehhh I need a little more of a description on how to do it, I'm still confused
anonymous
  • anonymous
For every x-value there is exactly one y-value. For example {(0,1), (1,5), (0, 3), (2, 4)} is not a function because for the x-value of 0, there are two y-values, 1, and 3.
anonymous
  • anonymous
I get it, so it's B!
anonymous
  • anonymous
By the example provided above, B cannot be a function because for the x-values of 3 and 4, there is more than one associated y-value. Check the others. What do you think?
anonymous
  • anonymous
It couldn't be A? Because it's only a x-value right? So that'd just leave C and D
anonymous
  • anonymous
That's right. For a the x-value of 1 has an infinite number of y-values. Check the others.
anonymous
  • anonymous
I have a feeling that the answer is D, if that's right could you explain to me why please?
anonymous
  • anonymous
Let's look at D. Are you able to rearrange it to solve for y?
anonymous
  • anonymous
Maybe, 16+4x^2=y?
anonymous
  • anonymous
Not quite\[4x^2 + y^2 = 16\]\[y^2 = 16 - 4x^2\]\[y=\pm \sqrt{16-4x^2}\]Are you able to follow that?
anonymous
  • anonymous
I don't really understand where you got the subtraction sign from when you first changed the equation. Can you explain what you did in this equation please?
anonymous
  • anonymous
The goal is to isolate y. Therefore, in the first step, I subtracted 4x^2 from both sides of the equation. Then to solve for y, I took the square root of both sides. Make sense?
anonymous
  • anonymous
Yeah, so what does this tell us? That there is only a value for the y?
anonymous
  • anonymous
OK. We've rearranged D to solve for y. So, choose an x-value - 0 would be a good choice. If you substitute 0 in for x, how many y-values do you get?
anonymous
  • anonymous
0 I guess? Sorry, I'm just not getting it as quickly as others probably would
anonymous
  • anonymous
Take the rearranged equation D and substitute 0 in for x\[y=\pm \sqrt{16-4x^2}\]\[y=\pm \sqrt{16-4\left( 0 \right)^2}\]\[y= \pm \sqrt{16}\]What's the answer for y?
anonymous
  • anonymous
You can do this. What's the square root of 16?
anonymous
  • anonymous
Oh that's easy, 4
anonymous
  • anonymous
Right. So, in equation D, if x=0, then y has to be +4 or -4. There are two y-values associated with x=0. Is this expression a function?
Mertsj
  • Mertsj
I think the square root of 16 is -4
anonymous
  • anonymous
Ummmm, no...no it's not...
anonymous
  • anonymous
You're incorrect @Mertsj . The square root of 16 is 4.
Mertsj
  • Mertsj
Must be because (-4)(-4)=16
Mertsj
  • Mertsj
Maybe 16 has two square roots.
anonymous
  • anonymous
Anyways, yes, it does represent a function
anonymous
  • anonymous
You're screwing up this help session. There is a mathematical distinction between answering a) what number, when squared, equals 16 b) what is the square root of 16 The answer to the first question is =4 and -4 The answer to the second question is 5.
Mertsj
  • Mertsj
The square root of a number is a number which multiplied by itself, gives you the original number.
anonymous
  • anonymous
The definition of a function is a relation in which, for every x-value there is ONE AND ONLY ONE associated y-value. We just determined that for x=0, there are two associated y-values, +4 and -4. Therefore, this expression cannot be a function. Do you understand.
Mertsj
  • Mertsj
Here is an easier definition of a function: A function is a set of ordered pairs in which no two ordered pairs have the same first number.
anonymous
  • anonymous
@Mertsj , what about {(1, 4), (3, 8), (1, 4), (1, 4)} ? You had better go back to school, chum.
anonymous
  • anonymous
@Mertsj Oh dieses Zeug langweilt mich bis auf die Knochen .
Mertsj
  • Mertsj
(1,4) and (1,4) are not two ordered pairs. It is one ordered pair written down twice. If you write your name twice, does that make you two people?
Mertsj
  • Mertsj
@RavenDarkwood200 Me too.
Mertsj
  • Mertsj
@RavenDarkwood200 Wie kann der Blinde den Blinden führt
anonymous
  • anonymous
@Mertsj Worüber redest du? Ich verstehe nicht. Ich bin deutscher sehen Sie?

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