This week in Pre-Calc 11 we learned about a cncept that is very hard for me, called “Rational Expressions. A rational expression is the quoient of two polynomials. This unit requires a lot of factoring, and also a lot of self control. By that I mean, you have to realyy stop yourself from simplifying any further, otherwise your answer will be completely wrong. This unit is especially hard when you are adding and subtracting rational expressions, because you have to find a common denominator with polynomials that have nothing in common. This unit requires a lot of thinking and practicing. The main thing to remember in this unit is that once you’ve done the necessary steps, don’t try to simplify any further. Also if you’re subtracting, always remember to disttibute your negative and change the correct signs to their opposites.

Here are some examples of rational expressions

This week in Pre-Calc 11 we worked with very weird looking graphs. We focused on absolute value functions and reciprocal functions. The weirdest ones we worked with were the quadratic reciprocal functions with 4 invariant points.

With absolute value functions you have to graph your equation, and then flip whatever is negative to it’s positive form. ex. (-2,-3) will flip to (-2,3), you only flip the y-value, not the x.

The most crazy thing we learned this week was the reciprocal functions. That’s where you put your equation under 1 and graph that. The most important points for this are the x-intercepts. The x-intercepts become your asymptotes. Asymptotes are the points on the graph that you can not touch or cross. The asymptotes can be represented as an electric fence. You can get as close as you want to it without getting shocked, but as soon as you touch it you get zapped. Asymptotes don’t just make one single point untouchable though. For example if the assymptote is y=2, you can not go below 2.

This is an example of a reciprocal function

This week in Pre-Calc we learned about Absolute Value Equations.  The main thing to know is that if it is an absolute value equation it can never be negative. Since it can never ever be negative you have to flip up the negative points when you graph it. Meaning when you graph the original equation (without thinking about absolute values), you need to mirror the negative points to make them positive for the absolute value equation. Another thing to know about Absolute Value Equations is piece-wise notation. Piece wise notation is when you make to equations that are the exact same, but for one of the equations you change the numbers in the absolute value braces to their opposites. To solve absolute value equations you should always isolate the numbers in the braces, and move all the numbers outside of it to the other side of the equation. After you’ve isolated it, you can get rid of the braces. Then solve the equation. To check plug your solution back into the equation.