Lucy needs to buy some organic apples, and her grocery store is having a sale on them. if she buys 3 or fewer pounds of apples, the price will be $1.50 per pound. if she buys more than 3 pounds of apples, the price is $1.10 per pound. what is the domain of the piecewise-defined function, where  x  represents the number of pounds of apples? a. {x|  x  ≥ 0}b. {x|  x  is a real number}c. {x| 0 ≤  x  ≤ 3}d. {x|  x  ≥ 3}

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is