[tex]f(x)=\left\{\begin{array}{lll}25 x& if & 0 < x\leq 7\\ 10x+105 & if & 7 < x\leq 17\\ 5x+190 & if & x > 17\end{array}[/tex]The piecewise function for the given situation is [tex]f(x)=\left\{\begin{array}{lll}25 x& if & 0 < x\leq 7\\ 10x+105 & if & 7 < x\leq 17\\ 5x+190 & if & x > 17\end{array}[/tex].
The correct option is C.
Given that the cost of renting a fishing boat is $25 per hour for the first 7 hours, $10 per hour for the next 10 hours, and $5 per hour for any additional hours.
A piecewise function is a function that has several curve segments in its graph. This means it has different definitions depending on the value of the input.
For first 7 hr, cost is 25/hr.
F(x)=25x
After 7 hr, until 10 hr, cost is 10/hr.
F(x)=10(x-7)+25×7
F(x)=10x-70+175
F(x)=105+10x
For addition hr, cost is $5/hr.
F(x)=5(x-17)+25×7+10(17-7)
F(x)=5x-85+175+10×10
F(x)=5x-85+175+100
F(x)=5x+190
So, the piecewise function is[tex]f(x)=\left\{\begin{array}{lll}25 x& if & 0 < x\leq 7\\ 10x+105 & if & 7 < x\leq 17\\ 5x+190 & if & x > 17\end{array}[/tex]
Hence, the piecewise function for the cost of renting a fishing boat is $25 per hour for the first 7 hours, $10 per hour for the next 10 hours, and $5 per hour for any additional hours is [tex]f(x)=\left\{\begin{array}{lll}25 x& if & 0 < x\leq 7\\ 10x+105 & if & 7 < x\leq 17\\ 5x+190 & if & x > 17\end{array}[/tex]
Learn more about the piecewise function from here brainly.com/question/1073355
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