The Science of Life Lecture Series

Hello internet, and welcome to the Algebra Lecture Series from the Science of Life.  This time, we are focusing on an introduction to the algebra of functions, or taking two or more functions and applying the algebraic functions in order to combine these functions. If we have two functions $f(x)$ and $g(x)$ which have the same domain, then applying the same x-value to them and performing a mathematical operation on them yields a single value.  It is important that they either have the same domain or have overlapping domain, since this is the only way that there would be a non-zero value for each function.  For example, a florist cannot physically store a negative quantity of flowers nor an amount of flowers greater than the physical space available.  Therefor, the domain is from 0 to some finite number determined by the physical space.  The same applies for other plants.  So flowers and plants have the same domain. One mechanism for applying an oper...

Hello internet, and welcome to the Algebra Lecture Series from The Science of Life.  This entry is focusing a little deeper into the concept of lines, especially the other equations of the line. Suppose that we have a line with slope $m$ and it passes through a specific point $(x_{1}, y_{1})$.  For any other general point (x, y) on the line (where $x_{1} \neq x$ and $y_{1} \neq y$) on the line, the slope of the line would be $m=\frac{y-y_{1}}{x-x_{1}}$.  Multiplying both sides of the equation by the denominator of the right hand side gives us $m \times (x-x_{1})=(y-y_1)$.  This final form is called the point-slope form of the linear equation, since we use a point and the slope. The two green lines are parallel. If we look at two parallel lines, they do not cross (they have no solution) by the definition of parallel lines.  This can only be done if the change in the y variable (the rise) for every unit change in the x variable are exactly the same ...