1.1: Analysis of Graphs
Functions can model real-life scenarios to determine the relationship among variables. One example is linear modeling, which can compare supply and demand models. This concept is used during the Christmas shopping season to see if the supply of the hot new toy is available to meet consumer demand. Nonlinear modeling occurs when the relationship fluctuates between the dependent and independent variables. An example is the number of bacteria growing in a petri dish, which can occur at an exponential rate. Functions can also be compared with the parent function by looking at the transformations of the function.
Subunit 1.1 contains a review of properties of functions and their graphs, including intercepts, symmetry, domain, and range. The properties discussed in this subunit will be applied to functions throughout the course.
Read this section on equations and graphs, stopping at "Review Questions." This reading discusses finding solutions to equations of graphs, intercepts, symmetry of graphs, points of intersection for the graphs, and linear models. Then, complete review questions 1-10 toward the bottom of the page. These exercises will provide you with the opportunity to identify intercepts and symmetry of the graph and represent linear modules. The solutions to these questions are located here.
Take notes as you watch these videos. Listen to the presentation carefully until you are able to explain the library of parent functions and relations. The functions include quadratics and logarithms and trigonometric and conic sections. You should also be able to explain how a function is graphed and discuss its properties using transformations.
Read this section on relations and functions. This reading discusses eight basic functions as well as the domain and the range for each function. There is also a review of material from the previous section. Then, complete review questions 1-10 toward the bottom of the page. These exercises will provide you with the opportunity to recognize the domain and range as well graph functions applying transformations. The solutions to these problems are located here.
Read this material describing an initial model. Watch all of the videos in this section and run each of the applets to see examples of functions. This literacy component will allow you to explore an application of a growth model function.
Read this material describing a rational function model. Watch all of the videos in this section and run each of the applets to see examples of functions. This literacy component will allow you to explore a realistic example of a rational function.