a. Graph -f(x):
By the transformations rules for functions, the graph of -f(x) is equal to a reflection over the x-axis, and a change of the y-coordinates:
[tex](x,y)\rightarrow(x,-y)[/tex]
Then, given the function:
[tex]f(x)=\sqrt[]{x}[/tex]
The graph of -f(x) is:is
The domain of the function is the set of all possible x-values, then it is:
[tex]\lbrack0,+\infty)[/tex]
The range is the set of all possible values of the function, then it is:
[tex]\lbrack0,-\infty)[/tex]
b. Graph f(x+2)-4:
The transformation f(x+2) is an horizontal translation left 2 units.
And the transformation f(x+2)-4 is a vertical translation down 4 units.
Then, the coordinates of this graph in comparison to the given graph are:
[tex](x,y)\rightarrow(x-2,y-4)[/tex]
Then for the point (1,1) the new coordinates are (1-2,1-4)=(-1,-3).
For (4,2): the new coordinates (4-2,2-4)=(2,-2)
For (9,3): the new coordinates (9-2,3-4)=(7,-1)
The graph is:
The domain of this function is:
[tex]\lbrack-2,+\infty)[/tex]
And the range is:
[tex]\lbrack-4,+\infty)[/tex]
