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After completing this course, Â鶹´«Ã½s can. . .

1. Simplify or manipulate expressions involving polynomial, radical, exponential, or logarithmic terms using appropriate properties and rules
2. Use numeric or variable substitution while working with expressions
3. Determine whether two expressions, functions, or equations involving polynomial, radical, exponential, or logarithmic terms are equivalent and
   1. Use appropriate strategies, properties, and rules to show they are the same, if equivalent
   2. Find a counter example (i.e. an input where they differ in value or solution sets), if not equivalent
4. Solve equations involving linear, polynomial, radical, rational, exponential, or logarithmic expressions
   1. Utilize inverse functions or operators
   2. Utilize factoring and the zero-product property
5. State if a rule is a function and, if it is, determine if it has an inverse that is also a function and justify
6. Determine if a function is linear, quadratic, exponential, or none of these and provide justification
   1. Find a linear, polynomial, exponential, or logarithmic function with given graphical properties or a real-world situation (context)
   2. Change the form of a linear, quadratic, or exponential function to one that more easily answers a given question
7. Evaluate functions involving polynomial, radical, rational, exponential, or logarithmic expressions at given input values, or find input values that map to a given output value
8. Compose or decompose functions and know the definition of an inverse function
   1. Use function composition to show two functions are inverses.
   2. Show function decompositions are not unique by finding different decompositions of a given function.
9. Use the structure of a function involving polynomial, radical, rational, exponential, or logarithmic expressions to
   1. Justify claims about domain, range, and minimum or maximum values
   2. Sketch a graph of the function
   3. Explain practical meaning of constants or values given a real-world context