Question

Sketch an example of a relation with Domain {x | x ∈R} and Range {y | y ≥ -5, y∈R}. Is this sketch a function?

Answer 1

Can someone help me please?

Answer 2

x^2 - 5

Answer 3

@sourwing can you roughly show me the sketch of it?

Answer 4

@sourwing We are being asked to explain why is it a function, can you list some its characteristics for me? that makes it a function?

Answer 5

@sourwing

Answer 6

a relation is a function if it is well defined and defined everywhere.

well defined means that if x=y then f(x) = f(y)

defined everywhere means that for all x in the domain , f(x) exists.

Answer 7

one naive way to see well defined is if it passes the "vertical line test". Do you know about this?

Answer 8

Nope, can you explain the vertical line test?

Answer 9

if there is any spot that you can draw a line going straight up and down, and this lines passes through the graph more than once, then the graph does not represent a function

Answer 10

Does this happen on the graph that @sourwing drew?

Answer 11

imagine that he meant to draw it nice. not with all those crooked parts

Answer 12

its the graph \(y=x^2-5\)

Answer 13

I think I get the gist of you mean, the sketch is correct though right?

Answer 14

well it should look smooth, but that is not so easy to draw with the tools on the site.

Answer 15

alright, I think I get it, thank you so much :)

Answer 16

It should look like this

http://www.wolframalpha.com/input/?i=graph+y%3Dx%5E2-5

Answer 17

yep, that's right :D Thanks again!