PRECAL.MATH.2.L
Determine various types of discontinuities in the interval (-∞, ∞) as they relate to functions and explore the limitations of the graphing calculator as it relates to the behavior of the function around discontinuities.
Precalculus · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012
Standard Unwrapping
AI-generated as a starting point — sign in to edit.Vocabulary
discontinuitiesintervalfunctionsgraphing calculatorbehaviorfunction
Skills
- determine (types of discontinuities in the interval (-∞, ∞)) #dok2
- analyze (limitations of graphing calculator with respect to discontinuities) #dok3
- identify (points and types of discontinuities on a graph) #dok2
- evaluate (behavior of functions around points of discontinuity) #dok3
Learning Targets
- I can identify different types of discontinuities in a function within the interval (-∞, ∞). #dok2
- I can determine whether and where a function is discontinuous on its graph. #dok2
- I can examine and evaluate the behavior of a function near discontinuities. #dok3
- I can analyze how well a graphing calculator displays functions around discontinuities. #dok3
- I can critically evaluate limitations of graphing calculators in representing discontinuities. #dok3
Big Ideas
- Discontinuities can show important changes in the behavior of functions and may not always be apparent with technology alone.
- Understanding the types of discontinuities and the behavior of functions around them is essential for mathematical analysis and accurate interpretation of graphs.
Essential Questions
- What are the different types of discontinuities that can occur in functions?
- How can you determine where a function is discontinuous by looking at its graph or equation?
- What limitations might a graphing calculator have when graphing functions with discontinuities?
- How does the behavior of a function change near a point of discontinuity?
- In what ways can technology mislead you when analyzing the continuity of a function?