Exponential and Logarithmic Functions
---------------------------------------

Goals for Section 3.1 of the book
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Students should be able to do each of the following:
  
* Determine if a given function is one-to-one. The function can be given in graphical, tabular, or algebraic forms.

* Explicitly show that a function is one-to-one or demonstrate why a function is not one-to-one.

* Use the horizontal line test to determine if a function is one-to-one.

* Determine the inverse of a given function. The function can be given in tabular or algebraic forms.

* Determine the domain and range of the inverse of a function. The function can be given in graphical, tabular, or algebraic forms.

* Limit the domain of a function that is not one-to-one so that an
    inverse can be defined on the resulting restricted domain.


Goals for Section 3.2 of the book
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Students should be able to do each of the following:

* Use the definition of an exponential function to define a function describing a situation given in written, verbal, or graphical form.

* Use the properties and operations of exponential functions to solve for any variable in an expression that has exponential functions.

* Be able to graph exponential functions. Be able to compare and identify different exponential functions whose parameters differ.
    
* Convert and write any exponential function using base *e*.
  
* Solve compound interest problems given a written description of the situation.
    
* Solve exponential growth/decay problems given a written description of the situation. Be able to identify if a situation results in either growth or decay.
    
* Given a written description determine if an exponential function or a logistic growth function is appropriate.


  
Goals for Section 3.3 of the book
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Students should be able to do each of the following:

* Use the logarithm function to solve for a variable in an equation that has exponential terms.
    
* Determine the domain and range of a simple function that contains logarithmic terms.
    
* Determine the inverse of a simple exponential function.
    
* Determine the inverse of a function that contains logarithmic terms.
    
* Graph basic logarithmic functions.
    
* Solve for a variable in an equation that contains logarithmic terms.
    
* Recognize that :math:`\log(x)=\log_{10}(x)`.
    
* Recognize that :math:`\ln(x)=\log_e(x)`.


Goals for Section 3.4 of the book
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Students should be able to do each of the following:

* Use the properties of logarithms to solve for a variable in a
    variety of more complex forms:
  
  :math:`\log_a(u\cdot v)  =  \log_a(u) + \log_a(v),`
          
  :math:`\log_a\left(\frac{u}{v}\right)  =  \log_a(u) - \log_a(v),`
          
  :math:`\log_a\left(u^r\right) =  r\log_a(u).`
    
    
* Solve for a variable when multiple logarithms with different bases are present in an expression. (Either using the substitution method or the change of base formula.)
  
* Change the base for a logarithm to either base *e* or base 10 so an approximation can be found using a calculator.


Goals for Section 3.5 of the book
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Students should be able to do each of the following:

* Solve equations with multiple exponential terms.

* Determine inverses of complicated functions that have either exponential or logarithmic terms.

* Manipulate equations with exponentials and transform them into other forms. For example, transform an expression with exponential terms into a quadratic equation.

* Define relationships given written descriptions that include wither exponential or logarithmic terms.

* Determine the value of any or all parameters in a compound interest
    problem given a written description of the situation.
    
* Determine the value of any or all parameters in an exponential
    growth/decay problem given a written description of the
    situation. Be able to identify if a situation results in either
    growth or decay.
    
* Determine the value of any or all parameters given a written
    description of a logistic growth function.

Goals for Section 3.6 of the book
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Students should be able to do each of the following:

* Solve equations for various parameters.
  
* Solve equations for a variable.
  
* Construct equations from written descriptions.
  
* Determine logistic relationships given a written description.
  
* Identify growth vs decay given a verbal written description.