Question 907200
a. {{{ y =  abs(3x - 9) }}}

The x-intercept is {{{y=0}}}; {{{ 0 =  abs(3x - 9) }}} => {{{ 0 =  sqrt((3x - 9)^2) }}} => {{{ 0 = (3x - 9) }}} or {{{ 0 = -(3x - 9) }}}

so, if {{{ 0 = (3x - 9) }}} => {{{3x=9}}} => {{{x=3}}} 

or
 if {{{ 0 = -(3x - 9) }}} => {{{-3x+9=0}}} => {{{-3x=-9}}} => {{{x=-9/-3}}}=> {{{x=3}}} ...x-intercept is at ({{{3}}},{{{ 0 }}})


and y-intercept: set {{{x=0}}} 

{{{ y =  abs(3*0 - 9) }}} => {{{ y = sqrt(( - 9)^2) }}} => {{{y= 9 }}}...y-intercept is at ({{{ 0 }}},{{{ 9 }}})



{{{ graph( 600, 600, -10, 10, -10, 10,abs(3x - 9)) }}} 

 

 

b. 

{{{y = x^3 - 8 }}}

x-intercept: set {{{y=0}}}
{{{0= x^3 - 8 }}} => {{{8= x^3  }}}  => {{{root(3,8)= x  }}}=> {{{root(3,2^3)= x  }}}=> {{{x =2 }}} ...x-intercept is at ({{{2}}},{{{ 0 }}})


y-intercept: set {{{x=0}}} 

{{{y = 0^3 - 8 }}} => {{{y=-8}}}...y-intercept is at ({{{ 0 }}},{{{ -8 }}})


{{{ graph( 600, 600, -10, 10, -10, 10,x^3 - 8) }}} 



c. {{{y =  5  -	3/x  }}}

x-intercept: set {{{y=0}}}

{{{0 =  5  -3/x  }}}

{{{3/x =  5  }}}

{{{3 =  5x  }}}

{{{3/5 =  x  }}}....x-intercept is at ({{{3/5}}},{{{ 0 }}})


y-intercept: set {{{x=0}}} 

{{{y =  5  -3/0  }}}

{{{y =  5  -infinity  }}} ...there is no y-intercept


{{{ graph( 600, 600, -10, 10, -10, 10,5  -3/x,5) }}} 


has horizontal asymptote through {{{y=5}}} 

{{{5-3/x}}}->{{{5 }}}  as   {{{x}}}->{{{+- infinity}}}

vertical asymptote
 
{{{5-3/x}}} -> {{{(+-infinity)}}}   as   {{{x}}} -> {{{0}}}