Which function is correct?

The first four terms of a sequence are given.

7, 11, 15, 19, .....

The pattern of the sequence continues in the same manner.  Jontae creates a function, f, to calculate the xth
term of the sequence where f(1) = 7.  Which function did Jontae create?
A.)  f(x) = 4x
B.)  f(x) = x + 4
C.)  f(x) = 4x + 3
D.)  f(x) = 3(x + 1)

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You are looking for a function, so that when you substitute 1 in for x, the value of f(x) is equal to 7.

Try f(x) = 4x + 3
f(1) = 4(1) + 3  {substituted 1 in for x}
=  4 + 3  {multiplied 4 by 1}
= 7  {added}

When you substitute 1, in for x, into f(x) = 4x + 3, the value of f(1) is 7.

C.)  f(x) = 4x + 3 is the correct function.

Furthermore, if you substitute 2 in for x, f(2) should be equal to the second term, which is 11.
f(x) = 4x + 3
f(2) = 4(2) + 3  {substituted 2 in for x}
= 8 + 3  {multiplied 4 by 2}
= 11  {added}

Also, if you substitute 3 in for x, f(3) should be equal to the third term, which is 15.
f(x) = 4x + 3
f(3) = 4(3) + 3  {substituted 3 in for x}
= 12 + 3  {multiplied 4 by 3}
= 15  {added}

As you can probably guess, if you substitute 4 in for x, f(4) will be equal to the fourth term, which is 19.

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