$$y=\text{f}(x)+a$$ - 

Translation by $$a$$ in the $$y$$-direction.

$$y=\text{f}(x+a)$$ - 

Translation by $$-a$$ in the $$x$$-direction.

$$y=-\text{f}(x)$$ - 

Reflection in the $$x$$-axis.

$$y=\text{f}(-x)$$ - 

Reflection in the $$y$$-axis.

$$y={a}\text{f}(x)$$ - 

Stretch by scale factor $$a$$ in the $$y$$-direction.

$$y=\text{f}(ax)$$ - 

Stretch by scale factor $$1\over{a}$$ in the $$x$$-direction.

$$2\text{f}(x)+3$$ - 

Output of $$\text{f}(x)$$ is multiplied by $$2$$ then $$3$$ is added.

$$3\text{f}(x)+2$$ - 

Output of $$\text{f}(x)$$ is multiplied by $$3$$ then $$2$$ is added.

$$3\text{f}(x+2)$$ - 

Input has $$2$$ added before output is multiplied by $$3$$

$$2\text{f}(x+3)$$ - 

Input has $$3$$ added before output is multiplied by $$2$$

$$2\text{f}(3x)$$ - 

Input is multiplied by $$3$$ before output is multiplied by $$2$$

$$-2\text{f}(x)$$ - 

Output of $$\text{f}(x)$$ is multiplied by $$-2$$