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anonymous

  • one year ago

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

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  1. anonymous
    • one year ago
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    Please help, I'm stuck!

  2. anonymous
    • one year ago
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    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?

  3. jdoe0001
    • one year ago
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    how can you tell a function from just a relation? hint: recall your DOMAIN and RANGE sets

  4. anonymous
    • one year ago
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    Ehhh I need a little more of a description on how to do it, I'm still confused

  5. anonymous
    • one year ago
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    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.

  6. anonymous
    • one year ago
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    I get it, so it's B!

  7. anonymous
    • one year ago
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    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?

  8. anonymous
    • one year ago
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    It couldn't be A? Because it's only a x-value right? So that'd just leave C and D

  9. anonymous
    • one year ago
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    That's right. For a the x-value of 1 has an infinite number of y-values. Check the others.

  10. anonymous
    • one year ago
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    I have a feeling that the answer is D, if that's right could you explain to me why please?

  11. anonymous
    • one year ago
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    Let's look at D. Are you able to rearrange it to solve for y?

  12. anonymous
    • one year ago
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    Maybe, 16+4x^2=y?

  13. anonymous
    • one year ago
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    Not quite\[4x^2 + y^2 = 16\]\[y^2 = 16 - 4x^2\]\[y=\pm \sqrt{16-4x^2}\]Are you able to follow that?

  14. anonymous
    • one year ago
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    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?

  15. anonymous
    • one year ago
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    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?

  16. anonymous
    • one year ago
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    Yeah, so what does this tell us? That there is only a value for the y?

  17. anonymous
    • one year ago
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    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?

  18. anonymous
    • one year ago
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    0 I guess? Sorry, I'm just not getting it as quickly as others probably would

  19. anonymous
    • one year ago
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    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?

  20. anonymous
    • one year ago
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    You can do this. What's the square root of 16?

  21. anonymous
    • one year ago
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    Oh that's easy, 4

  22. anonymous
    • one year ago
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    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?

  23. Mertsj
    • one year ago
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    I think the square root of 16 is -4

  24. anonymous
    • one year ago
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    Ummmm, no...no it's not...

  25. anonymous
    • one year ago
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    You're incorrect @Mertsj . The square root of 16 is 4.

  26. Mertsj
    • one year ago
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    Must be because (-4)(-4)=16

  27. Mertsj
    • one year ago
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    Maybe 16 has two square roots.

  28. anonymous
    • one year ago
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    Anyways, yes, it does represent a function

  29. anonymous
    • one year ago
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    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.

  30. Mertsj
    • one year ago
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    The square root of a number is a number which multiplied by itself, gives you the original number.

  31. anonymous
    • one year ago
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    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.

  32. Mertsj
    • one year ago
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    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.

  33. anonymous
    • one year ago
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    @Mertsj , what about {(1, 4), (3, 8), (1, 4), (1, 4)} ? You had better go back to school, chum.

  34. anonymous
    • one year ago
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    @Mertsj Oh dieses Zeug langweilt mich bis auf die Knochen .

  35. Mertsj
    • one year ago
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    (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?

  36. Mertsj
    • one year ago
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    @RavenDarkwood200 Me too.

  37. Mertsj
    • one year ago
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    @RavenDarkwood200 Wie kann der Blinde den Blinden führt

  38. anonymous
    • one year ago
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    @Mertsj Worüber redest du? Ich verstehe nicht. Ich bin deutscher sehen Sie?

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