a band must have the right mix of instruments. use the graph of the step function to find the maximum number…

Explanation:

Step1: Identify the tuba value

We know the number of tubas is 4. So we look at the graph where the y - axis (Tuba Players) is 4.

Step2: Find the corresponding trumpet range

For the step where Tuba Players = 4, we look at the x - axis (Trumpet Players). The interval for Tuba = 4 is from an open circle (exclusive) to a closed circle (inclusive). Looking at the graph, when Tuba = 4, the maximum number of trumpet players (the right - most point of the step for Tuba = 4) is 16. Wait, no, let's re - examine. Wait, the points: when Tuba is 4, the step goes from, let's see the x - values. Wait, the first step: Tuba = 1, Trumpet from 0 (open) to 4 (closed). Tuba = 2, Trumpet from 4 (open) to 8 (closed). Tuba = 3, Trumpet from 8 (open) to 12 (closed). Tuba = 4, Trumpet from 12 (open) to 16 (closed). Wait, no, maybe I got the steps reversed. Wait, the y - axis is Tuba Players, x - axis is Trumpet Players. So for each step, the y - value (Tuba) is constant, and x (Trumpet) varies. Let's list the steps:

• When Tuba = 1: Trumpet is in (0, 4] (open at 0, closed at 4)
• Tuba = 2: Trumpet in (4, 8]
• Tuba = 3: Trumpet in (8, 12]
• Tuba = 4: Trumpet in (12, 16]
• Tuba = 5: Trumpet in (16, 20]
• Tuba = 6: Trumpet in (20, 24]
• Tuba = 7: Trumpet in (24, 28]
• Tuba = 8: Trumpet in (28, 32]

Wait, no, maybe the steps are increasing Tuba with increasing Trumpet? Wait, no, the graph: the first horizontal line (Tuba = 1) goes from x = 0 (open) to x = 4 (closed). Then Tuba = 2 from x = 4 (open) to x = 8 (closed). Tuba = 3 from x = 8 (open) to x = 12 (closed). Tuba = 4 from x = 12 (open) to x = 16 (closed). Wait, but when Tuba = 4, the closed circle is at x = 16? Wait, no, looking at the graph, the point for Tuba = 4 is a closed circle at x = 16? Wait, the graph has for Tuba = 4: the open circle is at some x, and closed at x = 16? Wait, maybe I misread. Wait, the user's graph: when Tuba is 4, the step is from, let's see the x - axis. The x - axis labels are 4, 8, 12, 16, 20, 24, 28, 32. The Tuba = 4 step: the open circle is at x = 12, and closed at x = 16? Wait, no, the points: for Tuba = 4, the open circle is at x = 12 (maybe) and closed at x = 16? Wait, no, let's look at the coordinates. The Tuba = 4 has a point (16, 4) as a closed circle? Wait, maybe I got the steps wrong. Wait, the correct way: when we have 4 tubas, we look at the step where y = 4. The x - values for y = 4: the step function for y = 4 has a maximum x - value (since we want the maximum number of trumpets) at the closed circle. Looking at the graph, when Tuba = 4, the maximum number of trumpets is 16? Wait, no, wait the next step: Tuba = 5 has a closed circle at x = 20? No, maybe I messed up the Tuba and Trumpet axes. Wait, the y - axis is Tuba Players, x - axis is Trumpet Players. So for each Tuba value, we have a range of Trumpet values. When Tuba = 4, we need to find the maximum Trumpet in that step. Looking at the graph, the step for Tuba = 4: the right - most point (closed circle) is at x = 16? Wait, no, let's check the points. The Tuba = 4 has a closed circle at (16, 4)? Wait, maybe the steps are:

Tuba = 1: Trumpet ∈ (0, 4]

Tuba = 2: Trumpet ∈ (4, 8]

Tuba = 3: Trumpet ∈ (8, 12]

Tuba = 4: Trumpet ∈ (12, 16]

Tuba = 5: Trumpet ∈ (16, 20]

Tuba = 6: Trumpet ∈ (20, 24]

Tuba = 7: Trumpet ∈ (24, 28]

Tuba = 8: Trumpet ∈ (28, 32]

So when Tuba = 4, the maximum number of trumpets is 16 (since the interval is (12, 16], so the maximum is 16). Wait, but let's confirm. If Tuba = 4, the step is from x = 12 (open) to x = 16 (closed), so the maximum number of trumpets is 16.

Answer:

16