Question 1085859
Suppose that {{{f(x) = x - 8}}} and {{{g(x) = -3x+4}}}.

(a) 
Solve {{{f(x) = g(x)}}}. What is the value of {{{f}}} at the solution? What point is on the graph of {{{f}}}? What point is on the graph of {{{g}}}?

{{{f(x) = g(x)}}}

{{{x - 8 = -3x+4}}}

{{{x +3x = 8+4}}}

{{{4x = 12}}}

{{{x=3}}}

the value of {{{f}}} at the solution:

{{{f(x) = 3 - 8}}}

{{{f(x) =  - 5}}}

and, the point is on the graph of {{{f}}} is ({{{3}}},{{{-5}}})

since {{{x=3}}} is the value for what {{{f(x) = g(x)}}}, the point on the graph of {{{g}}} is same, ({{{3}}},{{{-5}}}) and it is the intersection point



(b) Solve {{{f(x) > g(x)}}}.

{{{f(x) > g(x)}}}

{{{x - 8 > -3x+4}}}

{{{x +3x > 8+4}}}

{{{4x >12}}}

{{{x>3}}}


(c) Graph {{{f(x)}}} and {{{g(x)}}} in the same Cartesian plane. Label the intersection point.


{{{drawing( 600, 600, -10, 10, -10, 10,
circle(3,-5,.12), locate(3,-5,p(3,-5)),
locate(1.2,3,g(x)=-3x+4),locate(6,-3,f(x)=x-8),
 graph( 600, 600, -10, 10, -10, 10, x - 8 , -3x+4)) }}}