Question

A function, f, passes through the points (1,1), (2,7) and (3,25). A function, g, passes through the points (1,36), (2,43) and (3,50).

Select the correct answer.

Answer 1

As the value of x increases, the value of f(x) will eventually exceed the value of g(x) is the correct option.

Explanation:

A function, f, passes through the points (1,1), (2,7) and (3,25).

The equation of the function 'f' can be written as:

The f(x) is obtained by:

`f\left(x\right)=3f\left(x-1_\right)+4`

`f\left(4\right)=3f\left(3\right)+4=\left(25* 3\right)+4=75+4=79`

A function, g, passes through the points (1,36), (2,43) and (3,50).

The g(x) is obtained by:

`g\left(x\right)=g\left(x-1\right)+7`

`g\left(4\right)=g\left(4-1\right)+7=g\left(3\right)+7=50+7=57`

So, value of f(x) at x = 4 exceeds the value of g(x) at x = 4.

Therefore, as the value of x increases, the value of f(x) will eventually exceed the value of g(x) is the correct option.