how to solve this function and graph?

Question

The graph of , is reflected in the x axis and shifted to the left 3 units and up 4 units. What is the equation of the new graph?

Answer 1

Suppose you have a function f(x).
To reflect a graph around the x axis, you replace x with -x.
f(-x)
To move the graph left 3 units you replace x with x+3.
f(-(x+3)) = f(-x-3)
To move the graph up 4 units you add 4 to the end of it
f(-x-3) + 4

I hope that helps.