Writing the equation of a function given different transformations

The video tutorial explains how to apply transformations to functions, focusing on horizontal compression and vertical shifts. Horizontal compression involves multiplying by a number inside the function, while vertical shifts involve subtracting a number outside the function. The tutorial emphasizes understanding the placement of these transformations within the function to achieve the desired effect.

What is the final form of the function after applying the transformations described?

Why is the number 5 inside the function while the number 7 is outside?