Which polynomial function could be represented by the graph below?

f(x) = x^3 + x^2 – 6x
f(x) = x^3 – x^2 – 6x
f(x) = –2x^3 – 2x^2 + 12x
f(x) = –2x^3 + 2x^2 + 12x

we know that

Using a graph tool

I'm going to proceed to graph each case to determine the solution

case a)

see the attached figure N

case b)

see the attached figure N

case c)

see the attached figure N

case d)

see the attached figure N

therefore

the answer is the option

case c)

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.