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shelby1290

  • one year ago

For each relation, explain whether it is a function or not a function and why. Also state the domain and range. *pictures included

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  1. shelby1290
    • one year ago
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    Part e)

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  2. shelby1290
    • one year ago
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    Part f)

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  3. shelby1290
    • one year ago
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    Part G)

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  4. shelby1290
    • one year ago
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    Part H)

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  5. anonymous
    • one year ago
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    One way to determine if it is a function or not is the "vertical line test" put your pen on your paper veritcally and drag it across your graph from left to right, if there is more than one point at any given x-value you then it effectively failed the vertical line test and is not a function.

  6. shelby1290
    • one year ago
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    @Audeezy oh okay, we learned that method in class today. Anyways, for part e) I wrote: The x-value 1 is associated with two y-values (y=1 and y=5) and the x-value 3 is associated with y=2 and y=4 Domain: {XER|x= 1,3,5} Range: {YER|y=1,2,3,4,5}

  7. shelby1290
    • one year ago
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    am i correct?

  8. anonymous
    • one year ago
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    At a glance yes,

  9. shelby1290
    • one year ago
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    okay and for part f) i just wrote: it's a function because it passes the vertical line test. Domain: {XER} Range: {YER|y= >1} i added a horizontal line underneath the greater than sign to represent any number greater than 1. But again, i wasn't sure

  10. shelby1290
    • one year ago
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    |dw:1441933100405:dw|

  11. shelby1290
    • one year ago
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    @Audeezy ^

  12. jim_thompson5910
    • one year ago
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    to type out \(\Large y \ge 1\) you would write `y >= 1` the greater than sign comes before the equal sign

  13. shelby1290
    • one year ago
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    ahh okay thanks for the tip! :)

  14. jim_thompson5910
    • one year ago
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    also, for part e)'s range, you can say \[\Large \{y \in \mathbb{Z} | 1 \le y \le 5 \}\] where the fancy Z is the set of integers. So basically, y is an integer from 1 to 5. The roster notation is probably better though

  15. jim_thompson5910
    • one year ago
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    if you decide to go with roster notation, all you have to do is list the numbers in curly braces. No other symbols are needed so the range for part e) in roster notation is simply `{1,2,3,4,5}`

  16. shelby1290
    • one year ago
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    Okay and what does it mean when you have 1<=y<=5

  17. jim_thompson5910
    • one year ago
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    that specifies the values of y that it can take on y could be 1, 2, 3, etc all up to 5. Nothing higher than 5, nothing smaller than 1

  18. jim_thompson5910
    • one year ago
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    so let's say we had 100 different values in the range starting from 1 and ending at 100 roster notation would be {1,2,3,..., 98,99,100} or it could be \[\Large \{y \in \mathbb{Z} | 1 \le y \le 100 \}\] which is much simpler

  19. shelby1290
    • one year ago
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    Oh okay I see. How about for part G with the circle?

  20. shelby1290
    • one year ago
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    I drew a vertical line through the x-value 2

  21. shelby1290
    • one year ago
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    @jim_thompson5910 is it possible for a circular shape to be a function?

  22. jim_thompson5910
    • one year ago
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    the question is: does that vertical line pass through more than one point?

  23. shelby1290
    • one year ago
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    Yes it does

  24. jim_thompson5910
    • one year ago
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    because it does, it fails the vertical line test. So it's NOT a function if x = 2, what is the y output? You can only choose one output if it was a function

  25. jim_thompson5910
    • one year ago
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    think of a case where you plug in 20 degrees Celsius into a conversion function if you get 2 outputs (say 68 and 100) which do you go for? which is the true Fahrenheit degree equivalent?

  26. shelby1290
    • one year ago
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    I've never learned about outputs or conversion functions but i think I understand the gist of what you're trying to say....

  27. jim_thompson5910
    • one year ago
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    I'll be right back

  28. shelby1290
    • one year ago
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    Alright

  29. jim_thompson5910
    • one year ago
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    ok back. So basically, because my example has 2 outputs, we would NOT have a function since there is no clear single output

  30. shelby1290
    • one year ago
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    Okay I get that. So my reasoning would be because the x-value 2 has two y-values/outputs? How do i write the domain and range for this?

  31. jim_thompson5910
    • one year ago
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    what is the left most point on the circle?

  32. jim_thompson5910
    • one year ago
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    |dw:1441937590807:dw|

  33. jim_thompson5910
    • one year ago
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    what is the x coordinate for that point

  34. shelby1290
    • one year ago
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    (-3,0)

  35. jim_thompson5910
    • one year ago
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    actually it's not (-2,0), yeah it's (-3,0)

  36. shelby1290
    • one year ago
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    -3 is the x

  37. jim_thompson5910
    • one year ago
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    how about the point on the opposite side? |dw:1441937737554:dw|

  38. shelby1290
    • one year ago
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    (3,0)

  39. shelby1290
    • one year ago
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    the x is 3

  40. jim_thompson5910
    • one year ago
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    so x spans from x = -3 to x = 3 the domain would be the set of real numbers x such that x makes this inequality true \[\Large -3 \le x \le 3\] in math set notation, we'd say \[\Large \{x \in \mathbb{R} | -3 \le x \le 3 \}\]

  41. shelby1290
    • one year ago
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    Alright

  42. shelby1290
    • one year ago
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    Would that make the range just any real number ? {YER}

  43. jim_thompson5910
    • one year ago
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    are you sure? can y be 10? 100? 1000?

  44. shelby1290
    • one year ago
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    Oh wait. i think its... {YER|y=-3<=y<=3}

  45. jim_thompson5910
    • one year ago
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    drop the `y=` part

  46. shelby1290
    • one year ago
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    is that right?

  47. shelby1290
    • one year ago
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    okay

  48. jim_thompson5910
    • one year ago
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    the first part \(\Large y \in \mathbb{R}\) sets up what kind of number y is y is a real number

  49. jim_thompson5910
    • one year ago
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    the vertical bar says "such that"

  50. jim_thompson5910
    • one year ago
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    the rest states how y is restricted in this case, y is only allowed to take on values from -3 to 3

  51. jim_thompson5910
    • one year ago
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    and of course, the curly braces say this is all a set

  52. shelby1290
    • one year ago
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    My teacher told us to write x= or y= after the bar so its a habit for me

  53. jim_thompson5910
    • one year ago
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    ah I see

  54. jim_thompson5910
    • one year ago
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    I've honestly never seen that sort of notation used before

  55. shelby1290
    • one year ago
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    Oh really? That's strange hm idk For h) I wrote that it passes the vertical line test so its a function

  56. jim_thompson5910
    • one year ago
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    correct

  57. shelby1290
    • one year ago
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    I'm a little bit lost with the domain and range though

  58. shelby1290
    • one year ago
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    I thought it was both any real number for other x and y because the line extends

  59. shelby1290
    • one year ago
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    * for BOTH x and y because

  60. jim_thompson5910
    • one year ago
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    yeah it looks like this is a straight line x can take on any value (any number is possible as an input) y can take on any value (any number is possible as an output)

  61. shelby1290
    • one year ago
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    Like this, right? Domain: {XER} Range: {YER}

  62. jim_thompson5910
    • one year ago
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    yeah

  63. shelby1290
    • one year ago
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    Alrightyyy! thank you so much for helping me and staying patient lol

  64. jim_thompson5910
    • one year ago
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    you're welcome

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