Which graph represents the solution to the compound inequality?

–6 < 3x – 12 ≤ 9

second graph

Step-by-step explanation:

Solving the inequality

- 6 < 3x - 12 ≤ 9 ( add 12 to all 3 intervals )

6 < 3x ≤ 21 ( divide the intervals by 3 )

2 < x ≤ 7

The graph has an open circle at 2 and a closed circle at 7

This is represented on the second graph

step-by-step explanation:

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.