Question 998957
The function should be defined as
{{{f(x)}}}={{{system((1/4)x+5/4,2x+3,-3x+18)}}} {{{matrix(4,2," "," ",if,x<=a,if,a<x<=b,if,b<x)}}} .
That "if b>x" on the last line does not make sense.


{{{f(a)=(1/4)a+5/4}}}
If the function is to be continuous at {{{x=a}}} ,
for a<x<=b. the limit {{{lim(x->a,2x+3)=2a+3}}} must equal {{{f(a)}}} .
{{{2a+3=(1/4)a+5/4}}}-->{{{4(a+3)=4((1/4)a+5/4)}}}-->{{{8a+12=4(1/4)a+4(5/4)}}}-->{{{8a+12=a+5}}}-->{{{8a-a=5-12}}}-->{{{7a=-7}}}-->{{{a=-7/7}}}-->{{{highlight(a=-1)}}}


{{{f(b)=2b+3}}}
If the function is to be continuous at {{{x=b}}} ,
for b<x. the limit {{{lim(x->b,-3x+18)=-3b+18}}} must equal {{{f(b)}}} .
{{{2b+3=-3b+18}}}-->{{{2b+3b=18-3}}}-->{{{5b=15}}}-->{{{b=15/5}}}-->{{{highlight(b=3)}}}