Reciprocal functions & rational expressions

This post is a gamut of what we did during this week thus far.

On Monday, we did some mental math. Once again, I made some stupid arithmetic errors -- that's something I badly need to improve upon. Ugh.

As for the material we learned in class, it was about transformations using various stretches of functions:

y = a * f(x)
y = f(x * b)

We were also introduced (reminded?) to absolute value functions and their graphs. So, it was about manipulating functions and viewing graphs so we can visualize the solutions to the problem.

If y = abs(x) then we get something that looks like a big V on the Cartesian coordinate plane.

These transformations can be summarized as:

y = a * f(x) | vertical stretch a > 1 | y = 2f(x)
y = a * f(x) | vertical compression 0 < a < 1 | y = 1/2
y = f(b(x)) | horizontal compression b > 1 | y = f(2x)
y = f(b(x)) | horizontal stretch | y = f(1/2x)

On Tuesday, we learned about reflections. No, not the kind that we do on this blog but the kind that pertains to functions.

A function can flip across the x-axis when f(x) becomes -f(x) and f(x) flips across the y-axis when f(-x). We also messed around with inverse functions.


Reciprocals . . . stuff we learned way back in grade five, and stuff we messed around with in grade 9. For example, a/b --------> b/a

so f(x) --------> 1 / f(x)

For inverse functions, the denominator can never be zero (since division by zero is undefined). This is something useful to keep in mind, if we are to try and visualize the function in our head.

Well, that's about it.