Question

The graph of g(x)

Answer 1

Answer:

If f(x)=x^2 and you translate it's graph 8 units to the left and 2 units up, g(x)=(x^2+8)+2

Answer 2

Answer:  The required function rule for g(x) is $g(x)=(x+8)^2+2.$

Step-by-step explanation:  Given that the graph of g(x)  is f(x) translated to the left 8 units and up 2 units, where f(x) is given by

$f(x)=x^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We are to find the function rule for g(x).

We know that

if a function y=p(x) is translated h units left and k units up, then h is added to x and k is subtracted from y.

For the given function, we have

h = 8 and k = 2.

Therefore, we get from (i) that

$g(x)-2=(x+8)^2\\\\\Rightarrow g(x)=(x+8)^2+2.$

The graphs of f(x) and g(x) are shown in the attached figure below.

Thus, the required function rule for g(x) is $g(x)=(x+8)^2+2.$