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

Answer:

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

Step-by-step 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 $g(x)=x^2+1$.