Write an inequality for this graph? Please help me, these are the last two questions on my homework and I don't know how to do them. :(

Question

anonymous · Answer

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anonymous · Answer

Also please help with this one:
The graph of g(x) is f(x) translated to the left 8 units and up 2 units.  What is the function rule for g(x) given f(x) = x²?

john_es · Answer

For the figure, use two points to find the equation if the line were straight (going down), I choose, (5,1) and (0,6), so, in the form y=mx+n,
$$m=\frac{1-6}{5-9}=-1\
n=6$$
So now, you see that the point where the vertex appear is x=5. You also need the right part of the graph. This time, I choose (7,3) and (5,1) to obtain,
$$y=x-4$$Then
$$f(x)=\begin{cases}-x+6\ \ \text{if}\ \ x\leq5\
x-4\ \ \text{if}\ \ x>5\end{cases}$$

john_es · Answer

For the second problem, $$ g(x)=(x+8)^2+2 $$

anonymous · Answer

thank you so much

john_es · Answer

You're welcome ;).