Question 823268
<pre>
g(x) = -&#8730;<span style="text-decoration: overline">16-3x</span>

There are no asymptotes, since there are no denominators with variables.

y = -&#8730;<span style="text-decoration: overline">16-3x</span>

Find the y intercept by substituting 0 for x:

y = -&#8730;<span style="text-decoration: overline">16-3(0)</span>

y = -&#8730;<span style="text-decoration: overline">16</span>

y = -4

So the y-intercept is (0,-4)

Find the x-intercept by substituting 0 for y

0 = -&#8730;<span style="text-decoration: overline">16-3x</span>

Square both sides

 0 = 16-3x

3x = 16 

 x = {{{16/3}}}

So the x intercept is ({{{16/3,0}}},0) or ({{{5&1/3}}},0)

{{{drawing(400,400,-7,7,-7,7,graph(400,400,-7,7,-7,7),

circle(16/3,0,0.15),circle(16/3,0,0.13),circle(16/3,0,0.11),circle(16/3,0,0.09),circle(16/3,0,0.07),circle(16/3,0,0.05),circle(16/3,0,0.03),circle(16/3,0,0.01),
circle(0,-4,0.15),circle(0,-4,0.13),circle(0,-4,0.11),circle(0,-4,0.09),circle(0,-4,0.07),circle(0,-4,0.05),circle(0,-4,0.03),circle(0,-4,0.01) )}}}

Maybe we need a few more points

 x|y
 5|-1
-3|-5
 2|-3.6
 4|-2
-5|-5.6

{{{drawing(400,400,-7,7,-7,7,graph(400,400,-7,7,-7,7),
circle(5,-1,0.15),circle(5,-1,0.13),circle(5,-1,0.11),circle(5,-1,0.09),circle(5,-1,0.07),circle(5,-1,0.05),circle(5,-1,0.03),circle(5,-1,0.01),

circle(16/3,0,0.15),circle(16/3,0,0.13),circle(16/3,0,0.11),circle(16/3,0,0.09),circle(16/3,0,0.07),circle(16/3,0,0.05),circle(16/3,0,0.03),circle(16/3,0,0.01),
circle(0,-4,0.15),circle(0,-4,0.13),circle(0,-4,0.11),circle(0,-4,0.09),circle(0,-4,0.07),circle(0,-4,0.05),circle(0,-4,0.03),circle(0,-4,0.01),
circle(-3,-5,0.15),circle(-3,-5,0.13),circle(-3,-5,0.11),circle(-3,-5,0.09),circle(-3,-5,0.07),circle(-3,-5,0.05),circle(-3,-5,0.03),circle(-3,-5,0.01),
circle(2,-3.16227766,0.15),circle(2,-3.16227766,0.13),circle(2,-3.16227766,0.11),circle(2,-3.16227766,0.09),circle(2,-3.16227766,0.07),circle(2,-3.16227766,0.05),circle(2,-3.16227766,0.03),circle(2,-3.16227766,0.01),
circle(4,-2,0.15),circle(4,-2,0.13),circle(4,-2,0.11),circle(4,-2,0.09),circle(4,-2,0.07),circle(4,-2,0.05),circle(4,-2,0.03),circle(4,-2,0.01),
circle(-5,-5.56776436,0.15),circle(-5,-5.56776436,0.13),circle(-5,-5.56776436,0.11),circle(-5,-5.56776436,0.09),circle(-5,-5.56776436,0.07),circle(-5,-5.56776436,0.05),circle(-5,-5.56776436,0.03),circle(-5,-5.56776436,0.01)




 )}}}

Now we can sketch it:

{{{drawing(400,400,-7,7,-7,7,graph(400,400,-7,7,-7,7,-sqrt(16-3x)),
circle(5,-1,0.15),circle(5,-1,0.13),circle(5,-1,0.11),circle(5,-1,0.09),circle(5,-1,0.07),circle(5,-1,0.05),circle(5,-1,0.03),circle(5,-1,0.01),

circle(16/3,0,0.15),circle(16/3,0,0.13),circle(16/3,0,0.11),circle(16/3,0,0.09),circle(16/3,0,0.07),circle(16/3,0,0.05),circle(16/3,0,0.03),circle(16/3,0,0.01),
circle(0,-4,0.15),circle(0,-4,0.13),circle(0,-4,0.11),circle(0,-4,0.09),circle(0,-4,0.07),circle(0,-4,0.05),circle(0,-4,0.03),circle(0,-4,0.01),
circle(-3,-5,0.15),circle(-3,-5,0.13),circle(-3,-5,0.11),circle(-3,-5,0.09),circle(-3,-5,0.07),circle(-3,-5,0.05),circle(-3,-5,0.03),circle(-3,-5,0.01),
circle(2,-3.16227766,0.15),circle(2,-3.16227766,0.13),circle(2,-3.16227766,0.11),circle(2,-3.16227766,0.09),circle(2,-3.16227766,0.07),circle(2,-3.16227766,0.05),circle(2,-3.16227766,0.03),circle(2,-3.16227766,0.01),
circle(4,-2,0.15),circle(4,-2,0.13),circle(4,-2,0.11),circle(4,-2,0.09),circle(4,-2,0.07),circle(4,-2,0.05),circle(4,-2,0.03),circle(4,-2,0.01),
circle(-5,-5.56776436,0.15),circle(-5,-5.56776436,0.13),circle(-5,-5.56776436,0.11),circle(-5,-5.56776436,0.09),circle(-5,-5.56776436,0.07),circle(-5,-5.56776436,0.05),circle(-5,-5.56776436,0.03),circle(-5,-5.56776436,0.01)




 )}}}

Notice that it is the bottom half of a parabola:.  The top half of the
parabola, the dotted part below, has the equation y = +&#8730;<span style="text-decoration: overline">16-3x</span>.  It takes 
two separate equations to get the graph of the whole parabola:

{{{drawing(400,400,-7,7,-7,7,graph(400,400,-7,7,-7,7,-sqrt(16-3x)),
circle(5,-1,0.15),circle(5,-1,0.13),circle(5,-1,0.11),circle(5,-1,0.09),circle(5,-1,0.07),circle(5,-1,0.05),circle(5,-1,0.03),circle(5,-1,0.01),

circle(16/3,0,0.15),circle(16/3,0,0.13),circle(16/3,0,0.11),circle(16/3,0,0.09),circle(16/3,0,0.07),circle(16/3,0,0.05),circle(16/3,0,0.03),circle(16/3,0,0.01),
circle(0,-4,0.15),circle(0,-4,0.13),circle(0,-4,0.11),circle(0,-4,0.09),circle(0,-4,0.07),circle(0,-4,0.05),circle(0,-4,0.03),circle(0,-4,0.01),
circle(-3,-5,0.15),circle(-3,-5,0.13),circle(-3,-5,0.11),circle(-3,-5,0.09),circle(-3,-5,0.07),circle(-3,-5,0.05),circle(-3,-5,0.03),circle(-3,-5,0.01),
circle(2,-3.16227766,0.15),circle(2,-3.16227766,0.13),circle(2,-3.16227766,0.11),circle(2,-3.16227766,0.09),circle(2,-3.16227766,0.07),circle(2,-3.16227766,0.05),circle(2,-3.16227766,0.03),circle(2,-3.16227766,0.01),
circle(4,-2,0.15),circle(4,-2,0.13),circle(4,-2,0.11),circle(4,-2,0.09),circle(4,-2,0.07),circle(4,-2,0.05),circle(4,-2,0.03),circle(4,-2,0.01),
circle(-5,-5.56776436,0.15),circle(-5,-5.56776436,0.13),circle(-5,-5.56776436,0.11),circle(-5,-5.56776436,0.09),circle(-5,-5.56776436,0.07),circle(-5,-5.56776436,0.05),circle(-5,-5.56776436,0.03),circle(-5,-5.56776436,0.01),

graph(400,400,-7,7,-7,7,10,11,12,13,14,sqrt(16-3x*sqrt(sin(10x))/sqrt(sin(10x))))




 )}}}



Edwin</pre>