Answer
$P(x)=\left\{\begin{array}{ll}
\$0.49 && 0\lt x \leq 1\\
\$0.70 && 1\lt x \leq 2\\
\$0.91 && 2\lt x \leq 3\\
\$1.12 && 3\lt x \leq 3.5
\end{array} \right.$
See the image below.
Work Step by Step
According to the information given, we can write:
$P(x)=\left\{\begin{array}{ll}
\$0.49 && 0\lt x \leq 1\\
\$0.70 && 1\lt x \leq 2\\
\$0.91 && 2\lt x \leq 3\\
\$1.12 && 3\lt x \leq 3.5
\end{array} \right.$
For weight below $1oz$ the price is $49$ cents
Additional weight, that is below $2oz$ in total, will add up $21$ cents, so $70$ cents in total
Heavier letter weighting less than $3oz$ will cost additional $21$ cents; $91$ cents in total
And if the letter is heavier (but less than $3.5oz$) another $21$ cents will be added; $112$ cents total
See the image above for graph.
