They plot these points in the same coordinate plane using red ink. Students need to note that the two graphs above are inverse functions. Students need to know that the inverse of, the exponential function with base 2, is called the logarithmic function with base 2. The student formulates equations and inequalities based on exponential and logarithmic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. For example, students use graphing calculators to investigate the following functions.
Students use graphing calculators to investigate the following functions.
Given a function, students predict the effects of changes on the parent function. Students complete tables like the one below to investigate asymptotic behavior. Students use a similar approach to investigate changes in the parameters and asymptotic behavior of a logarithmic function. The student formulates equations and inequalities based on exponential and logarithmic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. Clarifying Activity Students formulate an exponential function for a problem similar to the following one and determine a reasonable domain and range.