Example of 20 PPs

Today the topic of class was inverses.  We discussed how the graph of an inverse is simply a reflection over the y=x axis.  Below are some example of that, along with the equation which generates the graph, as well as the inverse.

At first, I did not understand what Mr. Newman meant by "reflection" and I couldn't picture these in my head, so I went to this website to try some reflections and created these three pictures to help my understanding:



After that, I decided to test this out on real functions.  The graphs were made using the Desmos graphing calculator.  The red is the original function, the green is inverse, which you notice is reflected over the black line, or y=x.


y=sin(x)+3
y=sin^-1(x-3)
y=x


y=x^2-3
y=+/- sqrt(x+3)
y=x

For the two Desmos graphs, I graphed them by switching the x and y (Desmos can graph that!).  For this blog, I solved for y so that both equations were in a more standard form.

Example of 10 PPs

Today the topic of class was inverses.  We discussed how the graph of an inverse is simply a reflection over the y=x axis.  Below are some example of that, along with the equation which generates the graph, as well as the inverse.  (The graphs were made using the Desmos graphing calculator)

The red is the original function, the green is inverse, which you notice is reflected over the black line, or y=x.


y=sin(x)+3
y=sin^-1(x-3)
y=x


y=x^2-3
y=+/- sqrt(x+3)
y=x

Example of 5 PPs

Today we learned about functions and their inverses.  I learned that graphically, inverses are just a function reflected over the y=x line, but that doesn't always make a function.  Here are some examples of functions and their inverses (from the notes).

f(x) --> f^-1(x)

x^2 --> sqrt(x)
3x --> x/3
4x+1 --> (x-1)/4

Example of 0 PPs

Today was a good day.  I learned a lot about functions.  I enjoy Mr. Newman's math class (pleeeeease give me points!).