We have two pieces of the piecewise function shown.
Let us try to find equation for each.
part first:
here the graph is a straight line parallel to x axis passing through y at 4
So equation of the line parallel to x axis is given by y=a, where a is y intercept.
so equation for first part is y=4
Second part:
here graph is a slant line with coordinates (3,2) and (5,4)
so let us first find slope of this line using the formula:
[tex] slope = \frac{y2-y1}{x2-x1} [/tex]
plugging values:
[tex] slope = \frac{4-2}{5-3} [/tex]
slope = 1
now we use point slope form to get the required equation
[tex] y-y1= m(x-x1) [/tex]
[tex] y-2= 1(x-3) [/tex]
[tex] y= x-3+2 [/tex]
y=x-1
Answer :
[tex] f(x) = \left \{ {{4, if -1\leq x \leq1} \atop {x-1 , if 3\leq x \leq 5}} \right. [/tex]
