Question

Please help me with this, I really need it, 50 points!!!

Answer 1

`g(x)=√(x+6)+3`

Explanation:

We are told that the graph of y = g(x) is a transformation of the graph y = f(x). To determine the transformation, compare the vertices of both curves.

The vertex of f(x) is (-4, -2).

The vertex of g(x) is (-6, 3).

Comparing the vertices of function f(x) and function g(x), we can see that function g(x) is a translation of function f(x):

• Horizontal translation of 2 units left.
• Vertical translation of 5 units up.

When translating horizontally to the left, add the units to the x value of the function: f(x + a).

When translating vertically upwards, add the units to the function: f(x) + a.

Therefore, the equation for function g(x) is:

`\begin{aligned}g(x) &= f(x+2)+5\\&=√(x+4+2)-2+5\\&=√(x+6)+3\end{aligned}`