Function transformation descriptions. Game on.

Adding $7$ outside the function increases every output by $7$, so the graph shifts $7$ units up.

Subtracting $3$ outside the function decreases every output by $3$, so the graph shifts $3$ units down.

Replacing $x$ with $x + 5$ is equivalent to $f(x - (-5))$, so the input must be $5$ smaller to produce the same output and the graph shifts $5$ units left.

Multiplying the outputs by $2$ doubles every $y$-value while leaving $x$-values unchanged, so the graph is stretched vertically by a factor of $2$.

Multiplying every output by $\dfrac{1}{3}$ pulls the graph toward the $x$-axis, so it is compressed vertically by a factor of $\dfrac{1}{3}$.

Replacing $x$ with $3x$ means outputs occur at one-third the original input values, so the graph is compressed horizontally by a factor of $\dfrac{1}{3}$.

Replacing $x$ with $-x$ pairs each input with its opposite, which reflects the graph across the $y$-axis.

Multiplying the outputs by $-1$ replaces each $y$-value with its opposite, which reflects the graph over the $x$-axis.