Function Fun, Shifting

By multiplying the function by a constant you can scale the function vertically while also adding a constant can shift the function up or down. This applet explores if modifying the independent variable of a function can be used to scale or shift a function horizontally. Several functions can be chosen by clicking the next button. The blue curve represents the modified function while the original function is shown lightly. Two sliders allow you to experiment with the constants. It is recommended to leave while adjusting and to leave while adjusting .
What happens as is increased? What happens as is increased? What happens when is negative? Are there non-zero values where the function is unchanged? Predict what would be different between and ?