Question

Postage rates Assume postage for sending a first-class letter in the United States is \$0.47 for the first ounce (up to and including 1 oz) plus \$0.21 for each additional ounce (up to and including each additional ounce).

a. Graph the function p=f(w) that gives the postage p for sending a letter that weighs w ounces, for 0<w≤3.5.

Accepted Answer

Step 1: Understand the problem. We need to graph the function p = f(w) that represents the postage cost p for a letter weighing w ounces, where 0 \u003c w ≤ 3.5. The cost is $$0.47 for the first ounce and 0.21 $$for each additional ounce. Step 2: Define the function. For 0 \u003c w ≤ 1, the cost is $$0.47. For 1 \u003c w ≤ 2, the cost is 0.47$$ + $$0.21 = 0.68. $$For 2 \u003c w ≤ 3, the cost is $$0.68 + 0.21$$ = $$0.89. For 3 \u003c w ≤ 3.5, the cost is 0.89$$ + $$0.21 = 1.10. $$Step 3: Identify the type of function. This is a piecewise function, where each piece is constant over the intervals (0, 1], (1, 2], (2, 3], and (3, 3.5]. Step 4: Plot the graph. On the x-axis, represent the weight w in ounces, and on the y-axis, represent the postage cost p in dollars. Plot horizontal line segments for each interval: from (0, 1] at $$0.47, from (1, 2] at 0.68$$, from (2, 3] at $$0.89, and from (3, 3.5] at 1.10. $$Step 5: Indicate the endpoints. Use closed circles at the right endpoints of each interval to indicate that the value is included, and open circles at the left endpoints (except for the first interval) to indicate that the value is not included.

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주요 개념

Piecewise Functions

Graphing Functions

Linear Functions