Wite an equation for the function graphed below Write an equ

Wite an equation for the function graphed below Write an equation for the function graphed below 5thw) h(w) HW 7 6 54 3-2 1 .2 .3 .4

Solution

Both the graphs representpiecewise functions. Let us begin with the 1st graph. In the interval ( - , - 3), h (w) 0 when w - and h (w) when w - 3. Thus the function in this interval is h (w) = a/(w + 3) where a is an arbitrary positive constant.

In the interval ( -3, 4), h (w) -   when w - 3 and h (w)   when w 4 Also h (w) = 0 when w = 3 and w = 0 when h(w) = -1. Then , in the interval ( -3, - 4), we have h (w) = - 4( w - 3)/ ( w - 4) ( w + 3)

In the interval ( 4, ), h (w) 0 when w   and h (w) -   when w 4. Therefore, in the interval ( 4, ) , we have h (w) = a/ (w - 4) where a is an arbitrary negative constant.

The function in the 2nd graph is as under. Let g (u ) = v. Then the function in the 2nd graph is

i. In the interval (- , - 3) , v = a/(u + 3) where a is an arbitrary negative constant.

ii. In the interval ( -3, 4) , v = - 4 ( u -2)/ ( u -4) ( u + 3)

iii. In the interval (4, ) , v = a / ( u - 4) where a is a arbitrary negative constant