Ans(a):
We know that a function can't have repeated x-values.
In given table we see that there i no repeating x-value. That's why the given table represents function.
Ans(b):
We know that a function can't have repeated x-values.
So if in given table we see any repeating x-value then that may cause the given data set to not be a function.
like if we have 3, 4, 3, 11 in the input then it will not be a function.
Ans(c):
we can use two points say (3,5) and (4,7) to find the linear equation of the form y=mx+b
slope is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{7-5}{4-3}=2[/tex]
Noow plug value of m=2 and any point say (3,5) into y=mx+b
5=2(3)+b
5=6+b
-1=b
now plug m=2 and b=-1 in y=mx+b, we get y=2x-1
Hence required equation in function notation can be written as
f(x)=2x-1.
Now to prove that above function is correct, we just graph the given points from table and the obtained function.
We see that points lie on the grpah of f(x)=2x-1.
Which proves that our equation is correct.
