# Math Help - Functions and relations

1. ## Functions and relations

Hey guys, i need some help with a couple of questions.

1.) {(2,y): y is a subset of Z}. State the domain and range of each and state whether the relations are FUNCTIONS.

2.) Could someone please explain the meaning of {(x,y): y = 5 -x} more specifically what the (x,y) in the question denotes.

3.) State the largest possible domain and range for the function defined by the rule: y = sqrt(16-x^2). For this question i stated that the equation had to be greater than or equal to 0 but i got stuck when i got the solution, please help!

2. Originally Posted by andrew2322
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2.) Could someone please explain the meaning of {(x,y): y = 5 -x} more specifically what the (x,y) in the question denotes.
{(x,y): y = 5 -x} means: It is the set of ordered pairs (x, y) which all satisfy the condition: y = 5-x

3.) State the largest possible domain and range for the function defined by the rule: y = sqrt(16-x^2). For this question i stated that the equation had to be greater than or equal to 0 but i got stuck when i got the solution, please help!
1. Domain: The radicand (That's the term under the root sign) must greater or equal zero:

$16-x^2\geq0~\implies~x^2\leq 16~\implies~-4 \leq x \leq 4$

2. Range: Since the radicand is smaller or equal 16 and it is greater or equal zero, you'll get: $0\leq y \leq 4$

3. ## thanks

hey thanks for the response, i don't quite understand what 'ordered pairs' means and what do you mean by satisfies 5-x?

and how did you get x is greater than or equal to -4 or less than or equal to 4? Wouldn't you get x is less than or equal to + or - 4?

4. 1.) Hey guys, i need some help with a couple of questions.

1.) {(2,y): y is a subset of Z}. State the domain and range of each and state whether the relations are FUNCTIONS.

2.) Could someone please explain the meaning of {(x,y): y = 5 -x} more specifically what the (x,y) in the question denotes.

3.) State the largest possible domain and range for the function defined by the rule: y = sqrt(16-x^2). For this question i stated that the equation had to be greater than or equal to 0 but i got stuck when i got the solution, please help!
first you understand the concept of functions and relations
functions and relations are 2 separate things
A function can be a relation but a relation is not necessary a function
the only thing which separate them apart is that
In relation a variable in domain-set can possess two values in range-set
but
In function a variable in domain-set can not possess two values in range-set, but two variable in domain-set can possess one values in range-set
1.) {(2,y): y is a subset of Z}. State the domain and range of each and state whether the relations are FUNCTIONS.
The above statement gives you answer of first question

2.) Could someone please explain the meaning of {(x,y): y = 5 -x} more specifically what the (x,y) in the question denotes.
earboth has explained correct:
{(x,y): y = 5 -x} means: It is the set of ordered pairs (x, y) which all satisfy the condition: y = 5-x
here ordered pair (x,y) means that for every value of x in domain set there is a corresponding value of y in range set

5. ## thanks

thanks for that, buy why do they have to put (x,y) infront of every expression? its sooo confusing!

6. thanks for that, buy why do they have to put (x,y) infront of every expression? its sooo confusing!
jst to indicate that x refers to domain set and y refers to range set
and when function is applied on x then the outcome is y