The Science of Life Lecture Series

Hello internet, and welcome to the Algebra Lecture Series from The Science of Life.  In this entry, we move to the definition of an algebraic function. I feel it is a good idea to start with the definitions of domain and range.  The domain is defined as the set of all possible values for which the independent variable (the input, the x-value) can take up.  This is all possible values for the horizontal (x) axis.  The range is the set of all possible values for which the dependent variable (the output, the y-value) can take up.  This is all possible values for the vertical (y) axis. The blue horizontal axis (typically the x-axis) is the domain and the independent variable. The green vertical axis (typically the y-axis) is the range and the dependent variable. Now we move to the concept of a function.  A good definition of the function is any equation where each input value has exactly one output value.  The technical version of this is "any eq...

Graphs are an important part of Algebra since they allow us to visualize information from the equations of Algebra.  After all, we deal better with the visual than the equation.  When we have an equation of two variables, we can see how they relate to one another more readily in a graph than in an equation. The course of Algebra focuses on the concept of functions (which will be defined in Section 2; because yes, functions are different than equations).  Most of the graphs considered here are what is called linear equations, equations which produce lines.  This chapter has the purpose of not only teaching the basics of graphing functions, but also using them for problem solving. Section 1: Graphs Section 2: Functions Section 3: Linear Functions: Graphs and Models Section 4: Other Equations of Line Section 5: Other Equations of Lines Section 6: The Algebra of Functions That's the end of this section.  If you have any questions, please leave ...

Hello internet, and welcome to the Algebra Lecture Series from the Science of Life.  This entry is an introduction to algebraic problem solving.  In Algebra, there are five steps for problem solving, which I'll cover here. Familiarize yourself with the problem situation.  This is basically a situation of knowing what the context of the problem is.  Is the context taxes?  Grocery shopping?  Tipping?  Scaling up or down the ingredients of a cake to get a different size cake than what the recipe says the size will be?  Here are the sub-steps for this contexts step: Read the problem carefully.  Read it aloud if need be to understand the problem. List the information and state the question being asked.  Select variables to represent anything which is unknown and clearly state what the variables represent, and be descriptive about the statement. Obtain any relevant information and equations.  If you're painting a room, find the ...