Please help. studying for my final and i don't really get functions…
Determine which of the following are functions.
$$A. \left| x \right|+2=y-1$$
$$B. y ^{2}-2x=3$$
$$c. 3x-y \le2$$
$$D. 5x ^{2}-2x=y+1$$

Question

Please help. studying for my final and i don't really get functions…
Determine which of the following are functions.
$$A.     \left| x \right|+2=y-1$$
$$B.     y ^{2}-2x=3$$ 
$$c.     3x-y \le2$$
$$D.     5x ^{2}-2x=y+1$$

anonymous · Answer

in these examples, do you want y as a function of x?

anonymous · Answer

well the question says determine which ones are functions so I'm not really sure.

anonymous · Answer

isn't there a way to look at the equation and know which one is a function?

anonymous · Answer

yes...
solve for y in each... 
then determine that if there is more than 1 y value for a particular x value in the equation, then it is NOT a function...

anonymous · Answer

it looks like there is more than 1 answer according to the choices/examples you provided...

anonymous · Answer

let's try "A"... solve for y....

anonymous · Answer

ok so ill try to solve it and ill get back to you. and let you know what i did

anonymous · Answer

ok... tag me when u need help....

anonymous · Answer

ok thank you!

anonymous · Answer

@dpaInc already need help but what i did was to get y by itself and got is
$$\left| x \right|+3=y$$ but unsure what my next step is.

anonymous · Answer

ok.. that's fine...

anonymous · Answer

notice here, that for ANY x value, you will get a unique y value....
so is this a function?

anonymous · Answer

do you know about the vertical line test?

anonymous · Answer

yes it is a function right? since there could be multiple x's but not y

anonymous · Answer

correct... this is a function....

anonymous · Answer

do you know of the vertical line test?

anonymous · Answer

the points can't hit the line more than once right? and if it does hit it more than once it is not a function

anonymous · Answer

yes... and that's the way i do these problems... with a picture in my head...
so for example... in A, i know the graph looks like this. and if i draw a vertical line anywhere, the vertical line will hit the graph only at 1 point...|dw:1342812007641:dw|

anonymous · Answer

so for the last problem since it was an absolute value is that what made it a function?

anonymous · Answer

oh ok so i can just type it into my calculator and look at each problem?

anonymous · Answer

no... even without the absolute value, this would still be a function...

BUT, if the absolute value was with the y variable, then it would not be a function....

anonymous · Answer

so anytime the y is an absolute value it is automatically not a function?

anonymous · Answer

yes...

anonymous · Answer

ok and how about for exponents? are there any rules for those

anonymous · Answer

let's do an easy example... which of these is a function:

$\huge y=x^2 $
$\huge x=y^2 $

anonymous · Answer

y=x^2 right?

anonymous · Answer

correct... why is that second one NOT a function?

anonymous · Answer

because X is one number and y can equal multiple numbers

anonymous · Answer

right...:)

anonymous · Answer

so do you think your second example in your question is a function?

anonymous · Answer

ok cool! so for my problems b is not a function and c is a function and still working on d

anonymous · Answer

correct...

anonymous · Answer

and d is a function as well right?

anonymous · Answer

here's the thing with "c".... it is not an equation but it is an inequality... that means you'll need to shade above or below some curve (or line, in this case) to show the solution set....
will the vertical line hit more than 1 y-value in the solution set if you do the vertical line test?

anonymous · Answer

you're correct with "d"....

anonymous · Answer

for c either side i shade it will hit the y value more than once meaning it will not be a function, correct?

anonymous · Answer

yes...:) you are correct....

anonymous · Answer

so any time i get a inequality it will not be a function?

anonymous · Answer

yes.... but there are exceptions...
may i ask, what class is this?  algebra 1?

anonymous · Answer

its intermediate algebra for the junior college

anonymous · Answer

ok... that's fine...

anonymous · Answer

you'll probably get to the part where I said "there are exceptions" later on in this course...:)

anonymous · Answer

can we recap?  which are functions, which are not?

anonymous · Answer

i am at the end of the course so maybe the next class. the problems i posted were off my study guide for the final.

anonymous · Answer

so A is a function, B and C are not, and D is a function!

anonymous · Answer

yes... good luck on your final...:)
the things we did here you should definitely write down....

anonymous · Answer

looks good...:)

anonymous · Answer

I am! thank you so much for your help! i understand functions better now!

anonymous · Answer

yw...:)