Finding Zeros of a Function

The zeroes of functions is where the graph crosses x. To find zeroes of a function you set the equation equal to zero. Another way to do/say this is to set y equal to zero. Once you do this simply solve the equation for x. Some times you will get more than one answer and that's okay. When you get the same number multiple times that number has multiplicity. For example if you get the number two three times you would say 2 has a multiplicity of three and if 5 appeared seven times you would say five has a multiplicity of seven. Here is an example of finding zeroes. 

Piece Wise Functions

A piece wise function is when a function has two different formulas that are both defined on the domain of f. Even though they are two different equations they are looked at as one function. They are usually used to represent the negative and the positive numbers. For example one equation usually has the restriction of x<0 and the other equation is x>0. To graph a piecewise defined function you graph each equation as you would normally and then it is either considered continuous or discontinuous. A continuous graph is when you don't have to lift your pencil when tracing the graph. A discontinuous graph is disconnected in places. Here is an example of a piecewise function problem.

Superhero Transformations

Today I worked on superhero transformations. There are six superheroes, lady straightedge, pawabawa, robo-grow, captain abs, radical girl, and bipolar tommy. Lady straightedge represents a straight line, her equation is f(x) = x and she has nuclear fusion blasts from her eyes. Pawabawa is a parabola his equation is f(x) = x^2 and he has parabolic kinetic rays. Robo-grow is from the exponential family, her equation f(x) = 2^x and she has a ginormous robot suit. Captain abs represents absolute value his equation is f(x) = |x| And he has finger beams. Radical girl represents a square root her equation is f(x) = sqrt x and he has ninja skills with a sword. Lastly bipolar tommy represents Cubing and his equation is f(x) = x^3 and he has a curvy laser gun. All these superheroes and their powers helped to complete the missions.