Question

a reciprocal function is reflected across the x-axis , vertical stretch by a factor of 3 shifted 8 units left and 3 units up

Answer 1

Assume the function is f(x).

The reciprocal function is given by;

`(1)/(f(x))`

Hence, applying the given transformations on the reciprocal function;

`\begin{gathered} Reflected\text{ across the x-axis;} \\ (1)/(-f(x)) \\ \\ \\ Vertical\text{ stretch by a factor of 3;} \\ 3*(1)/(-f(x))=-(3)/(f(x)) \\ \\ \\ Shifted\text{ 8 units left;} \\ -(3)/(f(x+8)) \\ \\ \\ \\ Shifted\text{ 3 units up;} \\ -(3)/(f(x+8))+3 \end{gathered}`

Therefore, the reciprocal function with its transformations is;

`-(3)/(f(x+8))+3`