Write a function based on the given parent function and transformations in the given order.
Parent function: $y=\frac{1}{x}$
(1) Stretch vertically by a factor of 5 .
(2) Reflect across the $x$-axis.
(3) Shift downward 2 units.
The function based on the given parent function and transformations in the given order is $y=$

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Answer

So, the function based on the given parent function and transformations in the given order is $\boxed{y=-\frac{5}{x}-2}$.

Steps

Step 1 ：Start with the parent function, $y=\frac{1}{x}$.

Step 2 ：Stretch vertically by a factor of 5 to get $y=5*\frac{1}{x}$ or $y=\frac{5}{x}$.

Step 3 ：Reflect across the x-axis to get $y=-\frac{5}{x}$.

Step 4 ：Shift downward 2 units to get $y=-\frac{5}{x}-2$.

Step 5 ：So, the function based on the given parent function and transformations in the given order is $\boxed{y=-\frac{5}{x}-2}$.