UP:MA19.A2.20
Vocabulary
- Polynomial function
- Logarithmic function Trigonometric (sine and cosine) function
- Reciprocal function
- Radical function
- Period
- Midline
- Amplitude
- End Behavior
- Intervals
- Maximum
- Minimum
- Horizontal Asymptote
- Vertical Asymptote
- Inverse functions
Knowledge
Techniques for graphing.
Skills
Students are able to:
- Identify the type of function from the symbolic representation.
- Manipulate expressions to reveal important features for identification in the function.
- Accurately graph any relationship.
- Find the inverse of a function algebraically and/or graphically.
Understanding
Students understand that:
- Key features are different depending on the function.
- Identifying key features of functions aid in graphing and interpreting the function.
- A function and its inverse are reflections over the line y = x.
Body
- Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions. a. Graph polynomial functions expressed symbolically, identifying zeros when suitable factorizations are available, and showing end behavior. b. Graph sine and cosine functions expressed symbolically, showing period, midline, and amplitude. c. Graph logarithmic functions expressed symbolically, showing intercepts and end behavior. d. Graph reciprocal functions expressed symbolically, identifying horizontal and vertical asymptotes. e. Graph square root and cube root functions expressed symbolically. f. Compare the graphs of inverse functions and the relationships between their key features, including but not limited to quadratic, square root, exponential, and logarithmic functions.
