ANSWER:
(a)
(b)
STEP-BY-STEP EXPLANATION:
(a)
We must do the following transformation:
[tex]y=f(x)\rightarrow y=f(-x)[/tex]
In this case, reflects f(x) about the y-axis. The rule that follows the above, is like this:
[tex](x,y)\rightarrow(-x,y)[/tex]
We apply the rule to the points of the function and it would be:
[tex]\begin{gathered} \mleft(-4.2\mright)\rightarrow(4,2) \\ (0,4)\rightarrow(0,4) \\ (4,6)\rightarrow(-4,6) \end{gathered}[/tex]
We graph and we have:
(b)
We must do the following transformation:
[tex]y=g(x)\rightarrow y=-g(x)[/tex]
In this case, reflects f(x) about the x-axis. The rule that follows the above, is like this:
[tex](x,y)\rightarrow(x,-y)[/tex]
We apply the rule to the points of the function and it would be:
[tex]\begin{gathered} \mleft(-7,-2\mright)\rightarrow\mleft(-7,2\mright) \\ \mleft(-4,-5\mright?)\rightarrow\mleft(-4,5\mright) \\ \mleft(4,-1\mright)\rightarrow\mleft(4,1\mright) \end{gathered}[/tex]
We graph and we have:
