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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
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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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0One 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 xvalue you then it effectively failed the vertical line test and is not a function.

shelby1290
 one year ago
Best ResponseYou've already chosen the best response.1@Audeezy oh okay, we learned that method in class today. Anyways, for part e) I wrote: The xvalue 1 is associated with two yvalues (y=1 and y=5) and the xvalue 3 is associated with y=2 and y=4 Domain: {XERx= 1,3,5} Range: {YERy=1,2,3,4,5}

shelby1290
 one year ago
Best ResponseYou've already chosen the best response.1okay and for part f) i just wrote: it's a function because it passes the vertical line test. Domain: {XER} Range: {YERy= >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
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441933100405:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1to type out \(\Large y \ge 1\) you would write `y >= 1` the greater than sign comes before the equal sign

shelby1290
 one year ago
Best ResponseYou've already chosen the best response.1ahh okay thanks for the tip! :)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1also, 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
 one year ago
Best ResponseYou've already chosen the best response.1if 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
 one year ago
Best ResponseYou've already chosen the best response.1Okay and what does it mean when you have 1<=y<=5

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1that 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
 one year ago
Best ResponseYou've already chosen the best response.1so 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
 one year ago
Best ResponseYou've already chosen the best response.1Oh okay I see. How about for part G with the circle?

shelby1290
 one year ago
Best ResponseYou've already chosen the best response.1I drew a vertical line through the xvalue 2

shelby1290
 one year ago
Best ResponseYou've already chosen the best response.1@jim_thompson5910 is it possible for a circular shape to be a function?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1the question is: does that vertical line pass through more than one point?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1because 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
 one year ago
Best ResponseYou've already chosen the best response.1think 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
 one year ago
Best ResponseYou've already chosen the best response.1I've never learned about outputs or conversion functions but i think I understand the gist of what you're trying to say....

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1I'll be right back

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1ok back. So basically, because my example has 2 outputs, we would NOT have a function since there is no clear single output

shelby1290
 one year ago
Best ResponseYou've already chosen the best response.1Okay I get that. So my reasoning would be because the xvalue 2 has two yvalues/outputs? How do i write the domain and range for this?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1what is the left most point on the circle?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441937590807:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1what is the x coordinate for that point

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1actually it's not (2,0), yeah it's (3,0)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1how about the point on the opposite side? dw:1441937737554:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so 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
 one year ago
Best ResponseYou've already chosen the best response.1Would that make the range just any real number ? {YER}

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1are you sure? can y be 10? 100? 1000?

shelby1290
 one year ago
Best ResponseYou've already chosen the best response.1Oh wait. i think its... {YERy=3<=y<=3}

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1drop the `y=` part

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1the first part \(\Large y \in \mathbb{R}\) sets up what kind of number y is y is a real number

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1the vertical bar says "such that"

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1the rest states how y is restricted in this case, y is only allowed to take on values from 3 to 3

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1and of course, the curly braces say this is all a set

shelby1290
 one year ago
Best ResponseYou've already chosen the best response.1My teacher told us to write x= or y= after the bar so its a habit for me

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1I've honestly never seen that sort of notation used before

shelby1290
 one year ago
Best ResponseYou've already chosen the best response.1Oh really? That's strange hm idk For h) I wrote that it passes the vertical line test so its a function

shelby1290
 one year ago
Best ResponseYou've already chosen the best response.1I'm a little bit lost with the domain and range though

shelby1290
 one year ago
Best ResponseYou've already chosen the best response.1I thought it was both any real number for other x and y because the line extends

shelby1290
 one year ago
Best ResponseYou've already chosen the best response.1* for BOTH x and y because

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yeah 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
 one year ago
Best ResponseYou've already chosen the best response.1Like this, right? Domain: {XER} Range: {YER}

shelby1290
 one year ago
Best ResponseYou've already chosen the best response.1Alrightyyy! thank you so much for helping me and staying patient lol

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you're welcome
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