the required function is
.
step-by-step explanation:
from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).
it is a linear function because the value of y is decrease by one as the value of x increase by 1.
the slope of the function is
![m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-7}{)}=\frac{-3}{3}=-1](/tex.php?f=m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-7}{)}=\frac{-3}{3}=-1)
the slope of the function is -1 and the y-intercept is 4.
the slope intercept form is
![y=mx+b](/tex.php?f=y=mx+b)
where, m is slope and b is y-intercept.
![y=-1x+4](/tex.php?f=y=-1x+4)
![y=-x+4](/tex.php?f=y=-x+4)
therefore the required function is
. the graph of this function is shown below.