Question 206878
What are the x- and y- intercepts of {{{ y=3(2-sqrt(x))/x }}}
<pre><font size = 4 color = "indigo"><b>
To find the x-intercept, substitute 0 for y and solve for x:

{{{ y=3(2-sqrt(x))/x }}}

{{{ 0=3(2-sqrt(x))/x }}}

Multiply through by x 

{{{ 0=3(2-sqrt(x)) }}}

Divide both sides by 3

{{{ 0=2-sqrt(x) }}}

{{{sqrt(x)=2}}}

Square both sides:

{{{(sqrt(x))^2=(2)^2}}}

{{{ x=4 }}}

So the x-intercept is (4,0)

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To find the y-intercept, substitute 0 for x and solve for y:

Oh! oh! The denominator is {{{x}}} and it can never be {{{0}}},
so the graph of this fuchtion cannot have a y-intercept.

Here is the graph:

{{{drawing(400,400,-2,8,-2,8,

graph(400,400,-2,8,-2,8,3(2-sqrt(x))/x),circle(4,0,.15) )     }}}

As you can see it intercepts the x-axis at(4,0), marked with
a little circle.

Edwin</pre></b></font>