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?

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