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

- shelby1290

- chestercat

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- shelby1290

Part e)

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- shelby1290

Part f)

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- shelby1290

Part G)

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- shelby1290

Part H)

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- 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

@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

am i correct?

- anonymous

At a glance yes,

- 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

|dw:1441933100405:dw|

- shelby1290

@Audeezy ^

- jim_thompson5910

to type out \(\Large y \ge 1\) you would write `y >= 1`
the greater than sign comes before the equal sign

- shelby1290

ahh okay thanks for the tip! :)

- 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

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

Okay and what does it mean when you have 1<=y<=5

- 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

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

Oh okay I see. How about for part G with the circle?

- shelby1290

I drew a vertical line through the x-value 2

- shelby1290

@jim_thompson5910 is it possible for a circular shape to be a function?

- jim_thompson5910

the question is: does that vertical line pass through more than one point?

- shelby1290

Yes it does

- 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

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

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

I'll be right back

- shelby1290

Alright

- 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

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

what is the left most point on the circle?

- jim_thompson5910

|dw:1441937590807:dw|

- jim_thompson5910

what is the x coordinate for that point

- shelby1290

(-3,0)

- jim_thompson5910

actually it's not (-2,0), yeah it's (-3,0)

- shelby1290

-3 is the x

- jim_thompson5910

how about the point on the opposite side?
|dw:1441937737554:dw|

- shelby1290

(3,0)

- shelby1290

the x is 3

- 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

Alright

- shelby1290

Would that make the range just any real number ? {YER}

- jim_thompson5910

are you sure? can y be 10? 100? 1000?

- shelby1290

Oh wait. i think its...
{YER|y=-3<=y<=3}

- jim_thompson5910

drop the `y=` part

- shelby1290

is that right?

- shelby1290

okay

- 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

the vertical bar says "such that"

- 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

and of course, the curly braces say this is all a set

- shelby1290

My teacher told us to write x= or y= after the bar so its a habit for me

- jim_thompson5910

ah I see

- jim_thompson5910

I've honestly never seen that sort of notation used before

- 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

correct

- shelby1290

I'm a little bit lost with the domain and range though

- shelby1290

I thought it was both any real number for other x and y because the line extends

- shelby1290

* for BOTH x and y because

- 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

Like this, right?
Domain: {XER}
Range: {YER}

- jim_thompson5910

yeah

- shelby1290

Alrightyyy!
thank you so much for helping me and staying patient lol

- jim_thompson5910

you're welcome

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