Consider the function f(x) defined by the finite set f(x)={(−2,5),(0,4),(1,−3)}. Graph the function f(x) and the transformation g(x)=f(x)−4.

let's calculate it step by step.

I'll assume that the function we look for is quadratic, because we only got 3 points

I plotted the 3 points for checking the equation later, and some intuited insight. see screenshot 1

let's write the general form of quadratic equations:

f(x) = a*x² + b*x + c

our goal is to correctly determine a, b and c

since we know from the 2nd point that

f(0) = a*0² + b*0 + c = 4

we can say

c = 4

this one comes almost for free

now to the next point, the 3rd one

f(1) = a*1² + b*1 + 4 = -3

we can write it as

a + b + 4 = -3

we can rearrange that to

a = -b -7

lastly, to the first point

f(-2) = a*(-2)² + b*(-2) + 4 = 5

simplified to

4a -2b + 4 = 5

since sort of defined a, let's plug it into our newest equation

4*(-b-7) -2b +4 = 5

we just swapped a for what its equal to.

now we just got numbers and b's

simplify it to

-4b -28 -2b +4 = 5

-6b -24 = 5

-6b = 29

b = -29/6

now we use the exact value of b to plug it into the rather simple equation from earlier. into this one

a = -b -7

a = -(-29/6) -7

a = 29/6 -42/6

a= -13/6

now that we got a, b and c we can write the whole equation

f(x) = -13/6*x² -29/6*x +4

see the graphic check in screenshot 2

second part of the problem:

if we want to move the whole graph 4 units down, we effectivly just cancel the +4 part

g(x) = f(x) -4 = f(x) = -13/6*x² -29/6*x +4 -4

g(x) = -13/6*x² -29/6*x

see screenshot 3 for the graph

to find the unit price, we must figure out the cost of one item (in this case one dish towel).   to do this, we divide the total price ($7.92) by the number of items bought (for this problem it is 8, because there are eight dish towels in one pack).  

$7.92/8 = $0.99

therefore, the unit price, or the price of one dish towel, is $0.99.

hope this !