Question 1037111
I agree with your answers for parts (a), (b), and (c).
 
For (d), I say NO, because if it were symmetric with respect to the x-axis,
along with point (1,3) the graph should also contain its reflexion across the x-axis (1,-3),
y=4-x^2. expresses y as a function of x,
so for a given x value, such as x=1, there is only one value of y.
 
For (e), I agree with the YES answer,
because the fact that x appears only  squared, as {{{x^2}}}
meas that y will have the same value for x and -x,
so if the graph contains the point (x,y),
it must also contain the reflexion of (x,y) across the y-axis : the point (-x,y). 
 
For (f), I say NO, because if it were symmetric with respect to the x-axis,
along with point (1,3) the graph should also contain its reflexion across the origin: (-1,-3),
y=4-x^2. expresses y as a function of x,
so for a given x value, such as x=-1, there is only one value of y, y=3.