Answer
(a) Shifting the graph upwards by $8$
(b) Shifting the graph leftwards by $8$
(c) Stretching the graph by the factor of $2$ vertically and then shifting it upwards by $1$
(d) Shifting the graph to the right by $2$ and then downwards by 2
(e) Reflecting the graph with respect to $x$ axis
(f) Reflecting the graph with respect to the line $y=x$
Work Step by Step
(a) Shifting the graph upwards by $8$
This is because we add $8$ to $f$
(b) Shifting the graph leftwards by $8$
This is because we evaluate $f$ at $x+8$ which defines the leftward translation by $8$
(c) Stretching the graph by the factor of $2$ vertically and then shifting it upwards by $1$.
This is because we first multiply $f$ by $2$ which stretches it vertically by the factor of $2$ and then we add $1$ which defines the upward translation by $1$
(d) Shifting the graph to the right by $2$ and then downwards by 2
This is because we evaluate $f$ at $x-2$ which defines the rightward translation by $2$ and then we subtract $2$ from it which defines the downward translation by $2$.
(e) Reflecting the graph with respect to $x$ axis.
This is because the sign of every value of $f$ will change so every point of that graph will "pass" to the other side of $x$ axis.
(f) Reflecting the graph with respect to the line $y=x$.
This is because every point of the graph $(x,y)$ will have its' $x$ and $y$ exchanged i.e. it will pass to $(y,x)$ which will result in the reflection about the line $y=x$.
