4. Cost of Mailing a Letter The cost of mailing a letter depends up…

Answer

Based on the step function graph provided, the costs are as follows: for a 2.5-ounce letter, it costs 45 cents; for a 4-ounce letter, it costs 51 cents; and for a 0.43-ounce letter, it costs 41 cents.

Explanation

The image shows a step function, which is a graph that stays constant over certain intervals and then "jumps" to a new value. In this graph, the horizontal axis (x-axis) represents the weight of the letter in ounces, and the vertical axis (y-axis) represents the cost in cents.

1. Analyzing the 2.5-ounce Letter Find $2.5$ on the horizontal axis. Looking at the "steps," the horizontal line segment covering the weight range that includes $2.5$ aligns with $45$ on the vertical axis. $Cost(2.5) = 45 \text{ cents}$ This value corresponds to the horizontal line segment at the height of 45 on the cost axis.

2. Analyzing the 4-ounce Letter Locate $4$ on the horizontal axis. Following the steps upward, the segment covering the weight of $4$ ounces aligns with $51$ on the vertical axis. $Cost(4) = 51 \text{ cents}$ This indicates that both 3 and 4 ounces fall within the same price bracket of 51 cents.

3. Analyzing the 0.43-ounce Letter Locate $0.43$ on the horizontal axis. This value falls on the first step above the initial point, which aligns with $41$ on the vertical axis. $Cost(0.43) = 41 \text{ cents}$ A weight greater than 0 but less than or equal to 1 ounce matches a cost of 41 cents based on this graph.

Final Answer

The costs for the requested weights are:

1. 2.5 ounces: $\boxed{45 \text{ cents}}$
2. 4 ounces: $\boxed{51 \text{ cents}}$
3. 0.43 ounces: $\boxed{41 \text{ cents}}$

Common Mistakes

• Misinterpreting Open vs. Closed Circles: Students often get confused by the circles at the ends of the lines. A closed circle (filled-in dot) means that exact value is included in that step, while an open circle means that value is not included (and marks the start of a new price).
• Reading the wrong axis: Ensure you always find the weight on the horizontal axis first, then move vertically to see which cost level it hits. Avoid reading the cost axis as if it were the weight.