Question

write the function as a set of ordered pairs give the domain and rage of f
f(a) = r f(b)=q f(c) = t f(d) = r

Answer 1

Writing it as ordered pairs is easy. Here is an example: \((a,r).\) Now write \(f(x)=\{\text{Insert all the ordered pairs here.}\}\)

For domain, write "the domain of \(f(x)\) is \(\{x: x\in \{\text{Insert the elements which are used in the function.}\}\}.\)" For example, \(a\) is in the domain.

For range, write, "the range of \(f(x)\) is \(\{x: x \in \{\text{Insert the } f(x)'\text{s}\}\}.\)" For example, \(r\) is in the range.

Answer 2

In different contexts, there is different rigor to writing the domain and range of a function. So, it heavily varies from place to place. My answer is my personal preference. It may not be the exact way that the questioner wants you to respond. However, there is not an "exact" way unless plainly stated in an example.

Answer 3

ok thanks limitless i am still trying to understand this I am kind of dumb when it comes to higher math could you give a example pls

Answer 4

Limitless if i understand this it would be f(a,r) f(b,q) f(c,t) f(d,r)

Answer 5

Okay, here is an example with different symbols.
\(f(u)=v,\) \(f(j)=k,\) and \(f(p)=q.\) This function, \(f(x)\) (we're saying \(f(x)\) because it allows us to speak generally about the function) is represented by the set of ordered pairs \(\{(u,v), (j,k), (p,q)\}.\) (The curly braces are important; they represent a set.)

This is because the value \(u\) corresponds to the value \(v\) (since \(f(u)=v\)), the value \(j\) corresponds to the value \(k\) (since \(f(j)=k\)), and the value \(p\) corresponds to the value \(q\) (since \(f(p)=q\)). An ordered pair is just \((x, f(x))\) where \(f(x)\) is our function at \(x.\)

Does this explain the first part?

Answer 6

f{(a,r),(b,q),(c,t),(d,r)}

Answer 7

Just remove the \(f\) and you're all good. In English, you'd say, "The function \(f(x)\) is represented by the set of ordered pairs \(\{(a,r),(b,q),(c,t),(d,r)\}.\)"

Answer 8

Using my same example as before, the domain and range are:

\(D=\{u,j,p\}\) and \(R=\{v,k,q\}.\) The domain is all input values. The range is all output values. (You can be more verbose if needed when it comes to these things. Like I said, it's a matter of convention.)

I must leave for now. Goodluck and have a good day! :)