Question

The local market is selling fresh fruit in baskets. The weights and amounts charged are shown below. For fruit weighing greater than or equal to 0.01 pounds and less than or equal to 0.5 pounds, the amount charged is $2.00. For fruit weighing greater than 0.5 pounds and less than or equal to 1.0 pounds, the amount charged is $3.50. For fruit weighing greater than 1.0 pounds and less than or equal to 1.5 pounds, the amount charged is $5.00. For fruit weighing greater than 1.5 pounds and less than or equal to 2.0 pounds, the amount charged is $6.50. For fruit weighing greater than 2.0 pounds and less than or equal to 2.5 pounds, the amount charged is $8.00. Which graph represents the function described?

Answer 1

The graph is shown below.

Explanation:

Let x be the weight of fruit in pounds and P(x) be the price of fruit.

For fruit weighing greater than or equal to 0.01 pounds and less than or equal to 0.5 pounds, the amount charged is $2.00.

P(x) = $2.00 for 0.01 ≤ x ≤ 0.5

For fruit weighing greater than 0.5 pounds and less than or equal to 1.0 pounds, the amount charged is $3.50.

P(x) = $3.50 for 0.5 < x ≤ 1.0

For fruit weighing greater than 1.0 pounds and less than or equal to 1.5 pounds, the amount charged is $5.00.

P(x) = $5.00 for 1.0 < x ≤ 1.5

For fruit weighing greater than 1.5 pounds and less than or equal to 2.0 pounds, the amount charged is $6.50.

P(x) = $6.50 for 1.5 < x ≤ 2.0

For fruit weighing greater than 2.0 pounds and less than or equal to 2.5 pounds, the amount charged is $8.00.

P(x) = $8.00 for 2.0 < x ≤ 2.5

It is a piecewise floor function. We have open circle on left side of each floor except first floor because the sign of inequality in all other is < .

We have closed circle on right side of each floor because the sign of inequality is ≤ .

The graph is shown below.