Answer
$(a)$
$x$-intercept $B(9, 0)$
$y$-intercept $A(0,3)$
The graph has no symmetry. See the image below.
$(b)$
$x$ and $y$ intercepts $C(0,0)$
It has symmetry about $x$-axis
Work Step by Step
$(a)$ $y=3-\sqrt{x}$
For a better visualization, we can write the equation as: $y= -\sqrt{x}+3$
That is a graph of $y=\sqrt{x}$ reflected about $x$-axis and then moved upwards.
Let's first find $x$ and $y$ interceptions.
For $y$-intercept, $x=0$
$y=-\sqrt{0}+3=0+3=3$
We have point $A(0, 3)$
For $x$-intercept, $y=0$
$0=-\sqrt{x}+3$
$\sqrt{x}=3$
$x=9$
We have point $B(9, 0)$
The graph will have a form of $y=-\sqrt{x}$, moved $3$ units upwards, so we can sketch the graph roughly like shown in the $(a)$ image above. For a better approximation one can input several $x$ values to find corresponding $y$ values and plot the points.
The graph has no symmetry.
$(b)$ $x=|y|$
As we know, an absolute value of any real number gives us positive number. So we will have two possible solutions:
$x=y$
AND
$x=-y$
$y=-x$
In both cases we have the same $x$ and $y$ intercepts, that is $C(0, 0)$
So we have $x=y$ graph and reflection of this graph about $x$-axis. See the image $(b)$ above.
The graph is symmetrical about $x$-axis
