#### After completing this course, students can. . .

- Simplify or manipulate expressions involving polynomial, radical, rational, exponential, or logarithmic terms using appropriate properties and rules
- Use numeric or variable substitution while working with expressions
- Determine whether two expressions, functions, or equations involving polynomial, radical, rational, exponential, or logarithmic terms are equivalent and
- Use appropriate strategies, properties, and rules to show they are the same, if equivalent
- Find a counter example (i.e. an input where they differ in value or solution sets), if not equivalent

- Solve equations involving linear, polynomial, radical, rational, exponential, or logarithmic expressions
- Utilize inverse functions or operators
- Utilize factoring and the zero-product property

- State if a rule is a function and, if it is, determine if it has an inverse that is also a function and justify
- Determine if a function is linear, quadratic, exponential, or none of these and provide justification
- Find a linear, polynomial, exponential, or logarithmic function with given graphical properties or a real-world situation (context)
- Change the form of a linear, quadratic, or exponential function to one that more easily answers a given question

- 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
- Determine the average rate of change of a function over a given interval and provide the practical meaning of the average rate of change when given context
- Compose or decompose functions and know the definition of an inverse function
- Use function composition to show two functions are inverses.
- Use the structure of a function involving polynomial, radical, rational, exponential, or logarithmic expressions to
- Justify claims about domain, range, and minimum or maximum values
- Sketch a graph of the function
- Explain practical meaning of constants or values given a real-world context