MHF 4U Learning Goals and Success Criteria Unit 2a: Graphing Polynomial and Rational Functions Learning Goal I will be able to: • Describe key features of polynomial functions and make connections between representations of them. (PR1) • Describe key features of the graphs of rational functions and represent them graphically. (PR2) Success Criteria I can: • Compare the numeric, graphical and algebraic representations of polynomial functions. (PR1) • Describe key features of graphs of polynomial functions. (PR1) • Distinguish polynomial functions from graphs of other types of functions. (PR1) • Determine the roles of a, k, d, and c in transforming graphs of cubic and quartic functions. (PR1) • Determine an equation of a polynomial function or family of polynomial functions that satisfies a given set of conditions. (PR1) • Compare the properties of even and odd degree polynomial functions, and identify polynomial functions as even, odd or neither. (PR1) • Determine the key features of the graphs of reciprocal functions and make connections between the algebraic and graphical representations of the functions. (PR2) • Determine key features of rational functions that have linear expressions in the numerator and denominator and make connections between the graphical and algebraic representations of the functions. (PR2) • Sketch the graph of a simple rational function using key features given the equation for the function. (PR2) Test Information: Your test is Thursday, March 8th. You can come in during lunch if you think that you might need a bit of extra time. I will allow you to start writing at 11:20. You should not NEED extra time, but you are welcome to take it if it will make you feel less stressed! There is a more detailed test outline on the back of this sheet. These are the types of questions you can expect. To prepare well for this test, you should (in this order): • Review your notes, and makes study notes. We talked about a lot of theory, so be sure that you actually understand it! • Review/redo your quizzes and go through the examples in the notes and be sure that you can do them yourself. • Complete questions in the suggested review that you think you need to do. The text book should be your last stop, not your first! If you need help with anything, please contact me through Edsby, Remind, or email, or come in at lunch or before school on Wednesday! • • Questions to Expect • • • • • • • • Text book Questions: Identify functions as polynomial or not, given different representations (graphs, equations, tables) Choose one of two short answer question involving the properties of polynomial functions (turning points, zeros, degree, symmetry, end behaviours, etc.) Find the equation for a member of a family of polynomial functions in factored form. Create a possible graph of a polynomial function given a set of parameters. Graph a polynomial function using a table of key points and applying transformations, then state properties of the graph. Graph a function and its reciprocal, and state properties of the reciprocal function. Create a graph of a reciprocal given the graph of a function, and then explain your reasoning. Short answer question involving asymptotes, holes, etc. (5.2) 𝑎𝑥+𝑏 Graph a rational function of the form 𝑓(𝑥) = 𝑐𝑥+𝑑 given its equation, and state properties of the graph. Explain how to find the asymptotes and intercepts for rational functions, and then explain why. p. 185 #1 – 3, 6 – 8, 9bde p. 186 #1, 2, 5 p. 308 #1 – 3, 5, 6 p. 310 #1 – 3, 6