Question

The graph represents the piecewise function:

Answer 1

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:

`slope = (y2-y1)/(x2-x1)`

plugging values:

`slope = (4-2)/(5-3)`

slope = 1

now we use point slope form to get the required equation

`y-y1= m(x-x1)`

`y-2= 1(x-3)`

`y= x-3+2`

y=x-1

Answer :

`f(x) = \left \{ {{4, if -1\leq x \leq1} \atop {x-1 , if 3\leq x \leq 5}} \right.`