Answers
f(-4) = -18, f(-2) = -10, f(6) = 12 and f(-1) = -6 using the piecewise function.
What are piecewise functions?A function defined by numerous sub-functions, where each sub-function applies to a distinct interval in the domain, is known in mathematics as a piecewise-defined function (also known as a piecewise function, a hybrid function, or definition by cases). Instead of being a property of the function itself, piecewise definition is a means to express the function.
When the domain may be divided into intervals on which the property holds, the phrase "property holding piecewise for a function" is used, which is separate but related. This is a characteristic of the function itself, as opposed to the idea mentioned above.
Calculation:
f(-4) = 4(-4)-2 = -18 ∵-4≤-1
f(-2) = 4(-2)-2= -10 ∵-2≤-1
f(6) = [tex]\frac{1}{2}*6 + 9 = 12[/tex] ∵6>-1
f(-1) = 4(-1)-2 = -6 ∵-1≤-1
f(-4) = -18, f(-2) = -10, f(6) = 12 and f(-1) = -6 using the piecewise function.
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Answers
Answer:
The piecewise function for the taxi fare is:
[tex]F(t) = 2.60\cdot \left(\frac {m}{0.25}\right) ,\, 0\,mi\le m \le 0.25\,mi[/tex]
[tex]F(t) = 2.60 + 0.36\cdot \left(\frac{m}{0.2} \right)[/tex], [tex]m > 0.25\,mi[/tex]
Step-by-step explanation:
We must use the following piecewise function:
(i) The Topology Taxi Company charges 2.60 for the first quarter of a mile:
[tex]F(t) = 2.60\cdot \left(\frac {m}{0.25}\right) ,\, 0\,mi\le m \le 0.25\,mi[/tex] (1)
Where:
[tex]F(t)[/tex] - Taxi fare, in monetary units.
[tex]m[/tex] - Number of miles driven, in miles.
(ii) And 0.36 for each additional fifth of a mile:
[tex]F(t) = 2.60 + 0.36\cdot \left(\frac{m}{0.2} \right)[/tex], [tex]m > 0.25\,mi[/tex] (2)
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