a florist can make 3 bouquets from 1 box of flowers. use the graph of the step function to find how many…

a florist can make 3 bouquets from 1 box of flowers. use the graph of the step function to find how many bouquets they can make with only 3 boxes of flowers.

a florist can make 3 bouquets from 1 box of flowers. use the graph of the step function to find how many bouquets they can make with only 3 boxes of flowers.

Answer

Explanation:

Step1: Understand the rate

The florist makes 3 bouquets per 1 box. So for ( n ) boxes, bouquets ( = 3\times n ), but we use the step - function graph.

Step2: Locate 3 boxes on the graph

On the vertical axis (Boxes of Flowers), find the line segment corresponding to 3 boxes. The solid dot on this segment gives the number of bouquets. From the graph, when the number of boxes is 3, we look at the step - function. Since 1 box gives 3 bouquets, 2 boxes give ( 3\times2 = 6 )? Wait, no, wait. Wait, the x - axis is number of bouquets, y - axis is boxes of flowers. Wait, let's re - interpret: The y - axis is boxes of flowers, x - axis is number of bouquets. The step function: for a range of bouquets, the number of boxes is constant. We know that 1 box makes 3 bouquets. So for 3 boxes, since 1 box → 3 bouquets, 2 boxes → 6 bouquets? Wait, no, the graph: when y (boxes) = 1, x (bouquets) is from just above 0 to 3? Wait, no, the first step: y = 1 (boxes), x (bouquets) from 0 (open circle) to 3 (closed circle)? Wait, no, the first step: open circle at x = 0, closed at x = 3, y = 1. Then y = 2: open at x = 3, closed at x = 6? Wait, no, the second step: y = 2, open at x = 3, closed at x = 6? Wait, the third step: y = 3, open at x = 6, closed at x = 9? Wait, no, let's look at the graph again. The y - axis is "Boxes of Flowers", x - axis is "Number of Bouquets". The steps:

  • For y = 1 (1 box), x is from 0 (open) to 3 (closed). So 1 box makes up to 3 bouquets.
  • For y = 2 (2 boxes), x is from 3 (open) to 6 (closed). So 2 boxes make up to 6 bouquets.
  • For y = 3 (3 boxes), x is from 6 (open) to 9 (closed). Wait, but the problem says "how many bouquets they can make with only 3 boxes of flowers". Since 1 box → 3 bouquets, 2 boxes → 6 bouquets, 3 boxes → 9 bouquets? Wait, no, wait the graph: when y = 3 (boxes), the closed dot is at x = 9? Wait, no, looking at the graph, the third step (y = 3) has a closed dot at x = 9? Wait, no, the third step: y = 3, the closed dot is at x = 9? Wait, no, the first step: y = 1, closed at x = 3. Second step: y = 2, closed at x = 6. Third step: y = 3, closed at x = 9. Because the rate is 3 bouquets per box. So for 3 boxes, the number of bouquets is ( 3\times3=9 )? Wait, but let's check the graph. The y - axis is boxes, x - axis is bouquets. So when we have 3 boxes (y = 3), the x - value (bouquets) at the closed dot is 9.

Wait, another way: The florist can make 3 bouquets per box. So for ( b ) boxes, bouquets ( B = 3\times b ). For ( b = 3 ), ( B=3\times3 = 9 ). But let's check the graph. The step for ( y = 3 ) (3 boxes) has the closed dot at x = 9. So the number of bouquets for 3 boxes is 9.

Answer:

9