Vertical Stretches and Compression of Functions

When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function. But why?

That's because each of the same input have been changed to the output 2x or o.5 of the original functions.

Reference

Abramson, J. (2017). Algebra and trigonometry. OpenStax, TX: Rice University. Retrieved from https://openstax.org/details/books/algebra-and-trigonometry