Graphs of y=f(x) and y=-f(x)

Part A

Below is the graph of , where a is the value in the slider. Change the values of a and check what happens to the graph of f(x). What is the domain of g(x)? What is the relationship between the graphs of and ?

Part B

Change the values of to alter the graph of . What is the natural domain of ? What is the relationship between the graphs of and ?

Part C

Below is the graph of , what happens to the graph of f(x) as a changes? What is the relationship between the graph of and ?

Part D

Can you make a general conjecture regarding the graphs of and from your observations of the graphs of these pairs?