2. Represent and Investigate and identify a function is Make sense of problems and evaluate problems continuous given its graph or its persevere in solving them. involving continuity. algebraic equation Calculus: Concepts & Contexts Reason abstractly and quantitatively. Section 2.4 Construct viable arguments and critique the reasoning of others. Explain how and why the concept of limits and continuity are related. District constructed materials Model with math. Use appropriate tools strategically. Sketch functions given information about Attend to precision. intervals of continuity Look for and make use of structure. Look for and express regularity in Investigate and identify values for repeated reasoning. constants so that a piecewise function will be continuous at a given point Apply the Intermediate Value theorem to functions and their graphs Learning Objective Standards for Mathematical Practice The student will… Content Outline Instructional Materials 3. Analyze the limits Calculus: Concepts & Contexts Make sense of problems and Explain how and why the concept of limits and horizontal asymptotes are related. involving infinity Section 2.5 persevere in solving them. Explain how and why the concept of limits graphically, Reason abstractly and quantitatively. and vertical asymptotes are related. numerically, District constructed materials Construct viable arguments and Identify infinite limits given the graph of a algebraically, and in critique the reasoning of others. function or the equation of a function context. Model with math. Identify limits at infinity given the graph of Use appropriate tools strategically. a function or the equation of a function Attend to precision. Sketch the graph of a function given Look for and make use of structure. information about infinite limits and limits Look for and express regularity in at infinity repeated reasoning.
2. Represent and evaluate problems involving continuity. Investigate and identify a function is continuous given its graph or its algebraic equation Explain how and why the concept of limits and continuity are related. Sketch functions given information about intervals of continuity Investigate and identify values for constants so that a piecewise function will be continuous at a given point Apply the Intermediate Value theorem to functions and their graphs Calculus: Concepts & Contexts Section 2.4 District constructed materials Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with math. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Learning Objective The student will… Content Outline Instructional Materials Standards for Mathematical Practice 3. Analyze the limits involving infinity graphically, numerically, algebraically, and in context. Explain how and why the concept of limits and horizontal asymptotes are related. Explain how and why the concept of limits and vertical asymptotes are related. Identify infinite limits given the graph of a function or the equation of a function Identify limits at infinity given the graph of a function or the equation of a function Sketch the graph of a function given information about infinite limits and limits at infinity Calculus: Concepts & Contexts Section 2.5 District constructed materials Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with math. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.