Equations as Functions

sleepygirl

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Aug 6, 2012
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For each equation,
a. solve for the domain = {-1, 0, 3, 8}, and
b. determine if the equation is a function

For a., do I have to write 4 equations for four domains, and then write yes or no? Here are five example problems:
x + y = 16
xy = 240
y = -5
x = 8
x^2 - 4 = y
 
For each equation,
a. solve for the domain = {-1, 0, 3, 8}, and
b. determine if the equation is a function

For a., do I have to write 4 equations for four domains, and then write yes or no? Here are five example problems:
x + y = 16
xy = 240
y = -5
x = 8
x^2 - 4 = y

1. The domain is a set of 4 discrete (integer) numbers. I don't know what exactly you want to "solve"?

2. To b: If you define a function as \(\displaystyle \displaystyle{y = f(x), y \in \mathbb{R}}\),where f(x) is a term in x, you have to check if you get valid values for y for all substitutions of \(\displaystyle x \in domain\). That means:

\(\displaystyle \displaystyle{x+y=16~\implies~y=-x+16}\) If ou plug in the elements of the domain you'll get a real value for y. So the given set is actually a domain of this specific function.

3. You'll find that 2 of the given equations can't be functions on the given domain.
 
No, the problem is not badly worded, as long you know what "domain" means. There are not four different domains here. There is a single domain consisting of 4 x values. The simplest way to write a fuction is as a set of ordered pairs and that is what they are talking about. For x+ y= 16, y= 16- x so if x= -1, y= 17; if x= 0, y= 16; if x= 3, y= 13, and if x= 8, y= 8. The relation is {(-1, 17), (0, 16), (3, 13), (8, 8)}.

I do agree that "x= 8" is very pecuiar here. Since 8 is not in the domain, there can be no relation.
 
then ask beginning students to determine whether the alleged domain is indeed a domain is unnecessarily confusing

But, Jeff, we do not know exactly what they are asking because the exercise is unclear.

I agree with Halls, that it is possible that "solve" means "find the range". Listing all of the (x,y) pairs is a valid way to express (aka define) a function, but then part (b) would make no sense.

I agree with you and pappus that the exercise is unclear as stated. "Solve for the domain"?!

I would contact the instructor for clarification, if the original post truly reflects what the students received.
 
As for the x = 8, I have no clue what question was intended by that

I think that I do. It's a test of whether the student understands that the linear equation x = 8 does not represent a function.

I'm going to post a guess at the instructions, too (if for no other reason than to excite Denis).



For each equation,

(a) Is there a functional relationship ?

(b) If {-1, 0, 3, 8} is a valid domain, state the range; otherwise, explain why this set is not a valid domain.

x + y = 16

xy = 240

y = -5

x = 8

x^2 - 4 = y
 
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