# week 13 -Precalc11

This week we continued with unit 8 of reciprocal functions and graphing.  This is a new concept so it was a challenge to wrap my head around these new concepts and vocabulary.

In lesson 8.3 we learned the most in my opinion.  there were some new vocabulary with this unit to help us graph the function :

invariant points : points that don’t change.

hyperbola : the graph of a reciprocal function

horizontal asymptote : The y value that the parabola never touches

vertical asymptote : the x value that the parabola never touches.

the reciprocal of a function will always look like this :

$x+3$

into ->

$\frac{1}{x+3}$

It will always be a fraction under 1.

This new way of graphing was interesting which made it kind of fun to learn since it was different and we had to think about graphing in a new way.

In lesson 8.5 we did the same thing, but we now had to graph reciprocal QUADRATIC functions.  it’s similar to linear in the sense that their will be invariant points and asymptotes, but completely different in how we graph the parabolas.  sometimes there will be more then 2 invariant points like in $\frac{1}{x^2-4}$ there will be 4.  we have to be careful when drawing the asymptotes because there will now be 3 lines instead of 2.  like always $y=0$, but the x values will be 2 and -2.  By the end we will have 2 parabolas beside each other on quadrant 1 and 2, also a parabola facing down below in the middle.