This week in Pre-Calc, I had some trouble understanding how to solve absolute values in piecewise notation, and how to solve reciprocal questions. So, today I will explain the steps on how to solve these.

To solve for piecewise notation, first, you will put the equation in absoulute value form. Next, you will will find the zero of the equation (isolate for “x” if it is a linear equation, or factor if it is a quadratic equation). After you have done this, you will put the number that you got from solving for “x” on a number line. You will choose two (if there is one “x” value) or three (if there are two “x” values) test points on your number line. Once youo have tested the points (by putting them back into the original equation), and you have determined which points are negative and positive, you can write the equation in piecewise form. To do this, you write “y” and then “{” and multiply in a negative for the negative value, writing whether it is < or > where you “x” value or values are on the number line. And you will leave the positive points as the original equation, and write < or > to represent where on the numberline “x” is positive.

To solve a reciprocal function, first you will put it into a fraction. Next, you will take the original equation (not in a fraction), and find the NVP. To do this, you will find the zero (the equation cannot be equal to zero) of the equation, and do this by isolating “x” (linear) or by factoring (quadratic). Once you have found what “x” cannot equal, this will be your asymptote. After, you go one to the left from your asymptote and up or down (positive, up or negative, down) and go one to the right from the asymptote and one up or down. You will then draw the shapes (two if it is linear, or three, one is a parabola, if it is quadratic).