Curriculum / Math / 11th Grade / Unit 9: Limits and Continuity / Lesson 9
Math
Unit 9
11th Grade
Lesson 9 of 9
Jump To
Sketch functions given limits and continuity requirements.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
This lesson is aligned to the Learning Objectives and Essential Knowledge described in the College Board's AP Calculus AB and AP Calculus BC Course and Exam Description:
LO1.1A(b): EK1.1A1, EK1.1A2, EK1.1A3
LO1.1B: EK1.1B1
LO1.2A: EK1.2A1
Note: This lesson will also serve as the review for this unit.
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
For the function $${f(x)}$$, given below, determine the following:
Let $${f(x)}=\begin{Bmatrix} x^2-5 & x\leq 3 \\ x+2 & x>3 \end{Bmatrix}$$
Write your answers in limit notation.
Draw a picture of a function with the following properties:
$${\lim_{x\rightarrow a^+}f(x)\neq \lim_{x\rightarrow a^-}f(x)}$$
$${\lim_{x\rightarrow a^+}f(x) = f(a)}$$
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Draw the picture of a function where $${f(c)=\lim_{x\rightarrow c^+}f(x)}$$, but the limit at $${x=c}$$ does not exist.
Lesson 8
Topic A: Limits and Continuity
Graph, write, and evaluate linear piecewise functions.
Use interval and function notation to describe the behavior of piecewise functions.
Sketch a slope graph from a linear piecewise function.
Find limits, including left- and right-hand limits, on a function given graphically.
Define continuity of functions and determine whether a function is continuous on a particular domain.
Write and evaluate piecewise functions algebraically and graphically using parent functions.
State and evaluate limits algebraically.
Evaluate infinite limits and limits at infinity.
Create a free account to access thousands of lesson plans.
Already have an account? Sign In
See all of the features of Fishtank in action and begin the conversation about adoption.
Learn more about Fishtank Learning School Adoption.
Yes
No
Access rigorous, relevant, and adaptable math lesson plans for free