TESTING MESSED UP THE SCHEDULE FOR MONDAY AND TUESDAY
Algebra: Chapter 12-1 and 12-2, p 536 and p 542
Relations and functions and graphs
A relation is a set or ordered pairs. The domain of a relation is the set of first coordinates (the x’s). The range is the set of second (or y) coordinates.
A function is a relation that assigns one member of the domain EXACTLY one member of the range. In other words, one x can have ONLY one y value.
You can evaluate a function `f(x)=2x^2 + 5` for `f(2)` by substituting 2 for every x that you see. In our example then, `f(2)=2⋅4 + 5 = 13`
You can recognize a function with the vertical line test. You can find the domain and range of a function by seeing where the function is not defined. Good examples are `−`, we can’t take square roots of negative numbers and we cannot have `1/0` because that results in infinity or an undefined solution.
Here again, is a great link for Purplemath
Math-8: Chapter 12-8 (Monday) and Chapter Review (Tuesday)
Pyramid and Cone Volume
Just like the we did for cylinders and rectilinear prisms, we calculate the surface area of the base and multiply it by the height (or altitude). BUT, if we did just that, we’d end up with cylinders or rectilinear prisms. SO, we have to remember that the formula for the pyramids and cones is just a little different.
Volume, `V=(Base Area⋅height)/3`. The `1/3` is the ONLY different part. Remember, for cones, the area of the base is `A=πr^2` and for a pyramid, it will be the base of the rectangle, triangle, trapezoid, pentagon, hexagon, octagon or whatever shape it is!