Question

Identify the parent function for the function g (x) = x+9 from its function rule. Then graph g and identify what transformation of the parent function it represents.

Answer 1

The parent function of g(x) = x + 9 is the function f(x) = x.

The function f(x) = x is a linear function, that is, it has degree 1 (the higher exponent of the variable x is 1).

In order to get g(x) from f(x), we can see that the function value was increased by 9 units:

`g(x)=f(x)+9`

Adding 9 units to the function means we have a translation of 9 units up.

Therefore the correct option is the third one.

Graphing g(x), we have: