Function transformations. Game on.

To shift left, $x$ gets smaller but the height stays the same, so $4$ is added inside $f$. That is why you see $(x + 4)$.

Multiplying the outputs by $2$ doubles every $y$-value and leaves the $x$-values unchanged. The graph is stretched vertically by a factor of $2$.

Subtracting $5$ outside $f$ decreases every output by $5\textsf{.}$ The graph shifts down $5$ units.

To shift right, $x$ gets larger but the height stays the same, so $3$ is subtracted inside $f$. Adding $5$ outside $f$ is a separate move up.

Adding $9$ outside $f$ increases every output by $9\textsf{.}$ The graph shifts up $9$ units.

To shift left, $x$ gets smaller but the height stays the same, so $4$ is added inside $f$. Subtracting $2$ outside $f$ is a separate move down.

Subtracting $6$ outside $f$ decreases every output by $6\textsf{.}$ The graph shifts down $6$ units.

To shift right, $x$ gets larger but the height stays the same, so $6$ is subtracted inside $f$. Adding $1$ outside $f$ is a separate move up.