On this week, we had a team work activity, we graph and solve absolute value functions and equations at the whiteboard. This activity was very fun. We discussed with our team and we helped each other. It was good at teamwork. Also we learned Graphing Reciprocals of Linear functions and Graphing Reciprocals of Quadratic functions. In these parts, the equation is looked like y= Its parents function is y= x. The reciprocal function’s form is to reflect the parents function. For example, y= x+5 Its reciprocal  function is y= . In reciprocal functions, there are some important things, the graph of y= has no x-intercept because latex \frac{1}{x-1}$ is undefined when x=1. That is, x=1 is a non-permissible value. The line x=1 is a Vertical Asymptote; that is, a vertical line that the graph approaches but never reaches. This asymptote passes through the x-intercept of y=f(x). In a word, Horizontal asymptote is y=0, Vertical asymptote is x-intercept. When we are graphing the reciprocal function, we have to know invariant points. Invariant points is the points when the y is 1 and -1. In linear reciprocal functions, there is one vertical asymptote. But in quadratic functions, there are maximum of two vertical asymptote. When we graphing Reciprocal functions, first we have to graph parents function and to find the points when y= 1 and -1, and finally to find vertical, horizontal asymptote. In linear reciprocal functions, the invariant points is maximum of two but in quadratic reciprocal functions , the invariant points is maximum of four.

Graphing Linear Reciprocal function and Quadratic function.