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When shipping a package, there is a complex process to determine shipping costs. Simplistically, by two-day air, to ship a package that weighs a fraction of an ounce up to 3 pounds, it would cost [tex]$\$[/tex] 7.35[tex]$. If the package is just over 3 pounds up to 10 pounds, it would be $[/tex]\[tex]$ 14.35$[/tex]. Between 10 and 20 pounds, it would cost [tex]$\$[/tex] 19.45[tex]$ plus $[/tex]\[tex]$ 0.50$[/tex] per pound for the weight over 10 pounds.

This could be represented as a piecewise function:
[tex]
f(x) =
\begin{cases}
7.35 & \text{if } 0 \ \textless \ x \leq 3 \\
14.35 & \text{if } 3 \ \textless \ x \leq 10 \\
19.45 + 0.50(x-10) & \text{if } 10 \ \textless \ x \leq 20
\end{cases}
[/tex]

Choose the correct pieces:
Select one or more:
a. [tex]$f(x) = 7.35 \quad 0 \ \textless \ x \leq 3$[/tex]
b. [tex]$f(x) = 7.35 \quad 0 \ \textless \ x \ \textless \ 3$[/tex]
c. [tex]$f(x) = 14.35 \quad 3 \leq x \ \textless \ 10$[/tex]
d. [tex]$f(x) = 19.45 + (0.50)(x-10) \quad 10 \ \textless \ x \leq 20$[/tex]
e. [tex]$f(x) = 19.45 + (0.50)(x) \quad 10 \ \textless \ x \leq 20$[/tex]
f. [tex]$f(x) = 14.35 \quad 0 \ \textless \ x \leq 10$[/tex]

Sagot :

GinnyAnsweridn
To write the given piecewise function [tex]\( f(x) \)[/tex], let's carefully interpret the conditions provided:

1. For packages weighing between 0 and 3 pounds (inclusive), the cost is [tex]$7.35. 2. For packages weighing just over 3 pounds up to 10 pounds (inclusive), the cost is $[/tex]14.35.
3. For packages weighing between 10 and 20 pounds, the cost is [tex]$19.45 plus $[/tex]0.50 for each pound over 10 pounds.

Let's match these conditions to the given choices:

a. [tex]\( f(x) = 7.35 \quad 0
This correctly states that the cost is [tex]$7.35 for packages in the weight range \( 0 < x \leq 3 \). b. \( f(x) = 7.35 \quad 0
In summary, the correct pieces for the piecewise function are:

a. [tex]\( f(x) = 7.35 \quad 0 < x \leq 3 \)[/tex]
d. [tex]\( f(x) = 19.45 + (0.50)(x-10) \quad 10 < x \leq 20 \)[/tex]
f. [tex]\( f(x) = 14.35 \quad 3 < x \leq 10 \)[/tex]

Hence, the correct pieces are: a, d, f.
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