In chapter three, I learned about the nature of graphs. I learned that a circle has infinite symmetry. Some graphs may show a line of symmetry or point symmetry. In order to test if a line has symmetry at the x-axis, the y-axis, at y = x, or y = -x, I learned that you must pick a point that will solve the equation and test the point for the x-axis, the y-axis, at y = x, and y = -x. For example, in x2 + y = 3, I chose the point (1,2) because 12 + 2 = 3. To test for the x-axis I used, iff f(a,b)=f(a,-b) then (1,-2). If I plug these points, (1,-2) into the original equation, then the equation is false. Therefore it is not symmetrical at the x-axis. To test for the y-axis I used iff f(a,b)=f(-a,b) then (-1,2). This point makes the original equation true; therefore it is symmetrical at the y-axis. At y = x I used, iff f(a,b)=f(b,a) then (2,1). This point make the original equation false, therefore there is no symmetry at y = x. To test y = -x, I used iff f(a,b)=f(-b,-a), then (-2,-1). This point makes the original equation true, therefore there is symmetry at y = -x. I also learned that if the highest degree in a function is even, then the function is even. If the highest degree in the function is odd, then the function is odd. I learned about the families of graphs. They are as follows:
y = x y = x2 y = x3
y = Radical x y = [x] y = x
y = 1/x y = Cubed root of x
If the coefficient is greater than one, the values increase faster and the graph becomes steeper. If the coefficient is less than one, then the values will increase slower, and the graph will be less steep. If the coefficient is less than zero, then it is a vertical flip. Adding and subtracting numbers...