Question 697267
{{{f(x) = (x+6)/(x-7)}}}

Is point ({{{x}}},{{{y}}})=({{{5}}},{{{-12}}}) on the graph of {{{f(x)}}} or {{{y}}}

{{{f(x) = (x+6)/(x-7)}}}...plug in values for {{{x}}} and {{{y}}}

{{{-12 = (5+6)/(5-7)}}}

{{{-12 = 11/-2}}}

{{{-12 <> -5.5}}}....so, the point is not on a graph


if {{{x=1}}}, what is {{{f(x)}}}? what point is on the graph of f?

{{{f(1) = (1+6)/(1-7)}}}


{{{f(1) = 7/-6}}}

{{{f(1) = -1.1666666666666666666666666666667}}}

{{{f(1) = -1.17}}}


point is ({{{1}}},{{{-1.17}}})


if f(x)=2, what is x? what points are on the graph of f?

{{{2 = (x+6)/(x-7)}}}


{{{2(x-7)= (x+6)}}}

{{{2x-14= x+6}}}

{{{2x-x= 14+6}}}

{{{x= 20}}}

point is ({{{20}}},{{{2}}})

what is the domain of f?

since denominator is {{{(x-7)}}} it will be equal to zero if {{{x=7}}}; so, the domain is all real numbers {{{x}}} except {{{x=7}}}


{{{x-intercepts}}}: set {{{f(x)=0}}}

{{{0 = (x+6)/(x-7)}}}

{{{0(x-7) = x+6}}}

{{{0 = x+6}}}

{{{-6= x}}}......there is one {{{x-intercept}}} at ({{{-6}}},{{{0}}})

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

{{{f(0)= (0+6)/(0-7)}}}

{{{f(0)= 6/-7}}}

{{{f(0)= -0.86}}}....there is one {{{y-intercept}}} at ({{{0}}},{{{-0.86}}})


{{{drawing(600,600,-10,20,-20,20,grid(1),circle(5,-12,0.3),graph(600,600,-10,20,-20,20,(x+6)/(x-7)))}}}