shelby1290
  • shelby1290
For each relation, explain whether it is a function or not a function and why. Also state the domain and range. *pictures included
Mathematics
chestercat
  • chestercat
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shelby1290
  • shelby1290
Part e)
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shelby1290
  • shelby1290
Part f)
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shelby1290
  • shelby1290
Part G)
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shelby1290
  • shelby1290
Part H)
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anonymous
  • anonymous
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.
shelby1290
  • shelby1290
@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}
shelby1290
  • shelby1290
am i correct?
anonymous
  • anonymous
At a glance yes,
shelby1290
  • shelby1290
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
shelby1290
  • shelby1290
|dw:1441933100405:dw|
shelby1290
  • shelby1290
jim_thompson5910
  • jim_thompson5910
to type out \(\Large y \ge 1\) you would write `y >= 1` the greater than sign comes before the equal sign
shelby1290
  • shelby1290
ahh okay thanks for the tip! :)
jim_thompson5910
  • jim_thompson5910
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
jim_thompson5910
  • jim_thompson5910
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}`
shelby1290
  • shelby1290
Okay and what does it mean when you have 1<=y<=5
jim_thompson5910
  • jim_thompson5910
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
jim_thompson5910
  • jim_thompson5910
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
shelby1290
  • shelby1290
Oh okay I see. How about for part G with the circle?
shelby1290
  • shelby1290
I drew a vertical line through the x-value 2
shelby1290
  • shelby1290
@jim_thompson5910 is it possible for a circular shape to be a function?
jim_thompson5910
  • jim_thompson5910
the question is: does that vertical line pass through more than one point?
shelby1290
  • shelby1290
Yes it does
jim_thompson5910
  • jim_thompson5910
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
jim_thompson5910
  • jim_thompson5910
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?
shelby1290
  • shelby1290
I've never learned about outputs or conversion functions but i think I understand the gist of what you're trying to say....
jim_thompson5910
  • jim_thompson5910
I'll be right back
shelby1290
  • shelby1290
Alright
jim_thompson5910
  • jim_thompson5910
ok back. So basically, because my example has 2 outputs, we would NOT have a function since there is no clear single output
shelby1290
  • shelby1290
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?
jim_thompson5910
  • jim_thompson5910
what is the left most point on the circle?
jim_thompson5910
  • jim_thompson5910
|dw:1441937590807:dw|
jim_thompson5910
  • jim_thompson5910
what is the x coordinate for that point
shelby1290
  • shelby1290
(-3,0)
jim_thompson5910
  • jim_thompson5910
actually it's not (-2,0), yeah it's (-3,0)
shelby1290
  • shelby1290
-3 is the x
jim_thompson5910
  • jim_thompson5910
how about the point on the opposite side? |dw:1441937737554:dw|
shelby1290
  • shelby1290
(3,0)
shelby1290
  • shelby1290
the x is 3
jim_thompson5910
  • jim_thompson5910
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 \[\Large \{x \in \mathbb{R} | -3 \le x \le 3 \}\]
shelby1290
  • shelby1290
Alright
shelby1290
  • shelby1290
Would that make the range just any real number ? {YER}
jim_thompson5910
  • jim_thompson5910
are you sure? can y be 10? 100? 1000?
shelby1290
  • shelby1290
Oh wait. i think its... {YER|y=-3<=y<=3}
jim_thompson5910
  • jim_thompson5910
drop the `y=` part
shelby1290
  • shelby1290
is that right?
shelby1290
  • shelby1290
okay
jim_thompson5910
  • jim_thompson5910
the first part \(\Large y \in \mathbb{R}\) sets up what kind of number y is y is a real number
jim_thompson5910
  • jim_thompson5910
the vertical bar says "such that"
jim_thompson5910
  • jim_thompson5910
the rest states how y is restricted in this case, y is only allowed to take on values from -3 to 3
jim_thompson5910
  • jim_thompson5910
and of course, the curly braces say this is all a set
shelby1290
  • shelby1290
My teacher told us to write x= or y= after the bar so its a habit for me
jim_thompson5910
  • jim_thompson5910
ah I see
jim_thompson5910
  • jim_thompson5910
I've honestly never seen that sort of notation used before
shelby1290
  • shelby1290
Oh really? That's strange hm idk For h) I wrote that it passes the vertical line test so its a function
jim_thompson5910
  • jim_thompson5910
correct
shelby1290
  • shelby1290
I'm a little bit lost with the domain and range though
shelby1290
  • shelby1290
I thought it was both any real number for other x and y because the line extends
shelby1290
  • shelby1290
* for BOTH x and y because
jim_thompson5910
  • jim_thompson5910
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)
shelby1290
  • shelby1290
Like this, right? Domain: {XER} Range: {YER}
jim_thompson5910
  • jim_thompson5910
yeah
shelby1290
  • shelby1290
Alrightyyy! thank you so much for helping me and staying patient lol
jim_thompson5910
  • jim_thompson5910
you're welcome

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