Question

Help!

Do the ordered pairs below represent a relation, a function, both a relation and a function, or neither a relation nor a function?
(-3,0) , (0,-3) , (7,-10) , (9,-12)

A. function only
B. relation only
C. both a relation and a function
D. neither a relation nor a function

Answer 1

point 1 (-3,0)
when y=0, x=-3
point 2 (0,-3) y=-3 when x=0
y=mx+b
from second point b=-3
y=mx-3
from 1 point 0=m(-3)-3 ......m=-1
y=-x-3

Answer 2

now use this formula and see if it get the numbers....
1 ( -3,0) it works
2 (0,-3) it works
3 (7,-10).....y=-(7) -3=-10 it works
4 (9,-12).......y=-(9)-3= -12 it works
it is a function

Answer 3

Don't even know which way to do it. Will choose the easiest way:
Suppose:

\(\large\color{slate}{ a_{-3}=0 }\)
\(\large\color{slate}{ a_0=-3 }\)
\(\large\color{slate}{ a_7=-10 }\)
\(\large\color{slate}{ a_9=-12 }\)

now, starting from an index n=1

\(\large\color{slate}{ a_{1}=0 }\)
\(\large\color{slate}{ a_4=-3 }\)
\(\large\color{slate}{ a_{11}=-10 }\)
\(\large\color{slate}{ a_{13}=-12 }\)

the differences b/w:

\(\large\color{slate}{ a_{1},~a_4 }\) \(\large\color{teal}{ a_{4}=a_1+d(n-1) }\)
\(\large\color{teal}{ -3=0+d(4-1) }\)
\(\large\color{teal}{ -3=3d }\)
\(\large\color{teal}{ d=1 }\)

\(\large\color{slate}{ a_{4},~a_{11} }\) \(\large\color{teal}{ a_{11}=a_{4}+d(7-1) }\)
\(\large\color{teal}{ -10=-3+d(8-1) }\)
\(\large\color{teal}{ -7=7d }\)
\(\large\color{teal}{ d=-1 }\)

\(\large\color{slate}{ a_{11},~a_{13} }\) \(\large\color{teal}{ a_{13}=a_{11}+d(3-1) }\)
\(\large\color{teal}{ -12=-10+d(3-1) }\)
\(\large\color{teal}{ -2=2d }\)
\(\large\color{teal}{ d=-1 }\)