Answer:
[tex]f(x)=\left \{ {{29\,\,for \,\,x\,\leq 250 } \atop {29+0.35(x-250)\,\,for \,x>250}} \right.[/tex]
Step-by-step explanation:
If we call "x" the number of call minutes used with this plan, the piecewise function used to describe it must represent;
a) a constant value of 29 for any x value smaller than or equal to 250
b) a line with positive slope of 0.35 for the region with x larger than 250. The mathematical representation of such increasing straight line, should be given by a line of slope m = 0.35, and containing the point (250, 29) which is the starting point for this right hand side portion of the domain:
[tex]f(x)=0.35(x-250)+29\\f(x)=0.35 x-87.5+29\\f(x)=0.35 x-58.5[/tex]
So the function should look like:
[tex]f(x)=\left \{ {{29\,\,for \,\,x\,\leq 250 } \atop {29+0.35(x-250)\,\,for \,x>250}} \right.[/tex]
or as shown above, in a more simplified form:
[tex]f(x)=\left \{ {{29\,\,for \,\,x\,\leq 250 } \atop {0.35x-58.5\,\,\,for \,\,x>250}} \right.[/tex]
