Question

H(x) = x2 – 3

If the graph of h is translated vertically upward by 4 units, it becomes the graph of a function g.
Find the expression for g(x).

Answer 1

`g(x)=x^2+1`

Explanation:

The given function is

`h(x)=x^2-3`

If a function translated vertically upward by p units, then we need to add p in the function value to get the new function.

It is given that if the graph of h is translated vertically upward by 4 units, it becomes the graph of a function g. So,

`g(x)=h(x)+4`

`g(x)=x^2-3+4`

On simplification, we get

`g(x)=x^2+1`

Therefore, the required function is
`g(x)=x^2+1`.