Question

If g={(1,1),(2,3),(3,5),(4,7)} is a function
given by g(x)=Ax+B then the values of
A and B are
11 Doint​

Answer 1

Answer:

Yes, it is a function ( on the domain {1, 2, 3, 4} ).

a = 2, b = -1

Step-by-step explanation:

g is a function if for every element x in the domain, there is exactly one pair in g with x as the first component.

Here we have domain {1, 2, 3, 4}.

There is exactly one pair in g with a 1 in the first position, namely the pair (1,1).

There is exactly one pair in g with a 2 in the first position, namely the pair (2,3).

There is exactly one pair in g with a 3in the first position, namely the pair (3,5).

There is exactly one pair in g with a 4 in the first position, namely the pair (4,7).

So g is a function.

[ BTW The range is the set of values that turn up on the right hand side in the pairs.  Here the range is { 1, 3, 5, 7 }. ]

For the next bit, if g(x) = ax + b, then

g(1) = 1  =>  a + b = 1

g(2) = 3  =>  2a + b = 3

From here,  we get a = 2 and b = -1.  Still need to check that this always applies though:

3a + b = 6 - 1 = 5 = g(3)... good, the rule applies here!

4a + b = 8 - 1 = 7 = g(4)... good, the rule applies here, too!