Question

math 3 end - of - unit 1 assessment: piecewise functions
for questions 1 - 10, a scientific calculator may be used, but not a graphing calculator.
use the following information to answer questions 1 - 5.
the cost to mail a letter in the united states in 2022 is described by the function below, where c is cost in u.s. dollars and w is the weight of the letter in ounces.
c(w)=\

$$\begin{cases}0.60, & 0 < w \\leq 1 \\\\0.84, & 1 < w \\leq 2 \\\\1.08, & 2 < w \\leq 3 \\\\1.32, & 3 < w \\leq 4 \\\\1.56, & 4 < w \\leq 5 \\\\1.80, & 5 < w \\leq 6\\end{cases}$$

1. find c(4.5).

c(4.5)=\frac{1.56}{(numerical value)}

1. explain what c(4.5) means in context.

fill in the blanks below to correctly finish the statement.
a package that weighs \underline{(numerical value)} ounces will cost $\underline{(numerical value)} to mail.

1. find c(3).

c(3)=\frac{}{(numerical value)}

Explanation:

Step1: Identify the interval for $w = 4.5$

Since $4 < 4.5\leq5$, we use the formula $c(w)=1.56$ for this interval.

Step2: Find $c(4.5)$

$c(4.5)=1.56$

Step3: Explain $c(4.5)$ in context

$c(4.5)$ represents the cost to mail a letter that weighs 4.5 ounces. A package that weighs 4.5 ounces will cost $1.56$ to mail.

Step4: Identify the interval for $w = 3$

Since $2 < 3\leq3$, we use the formula $c(w)=1.08$ for this interval.

Step5: Find $c(3)$

$c(3)=1.08$

Answer:

1. $c(4.5)=1.56$
2. A package that weighs 4.5 ounces will cost $1.56$ to mail.
3. $c(3)=1.08$