Free 11th Grade Real Functions Lesson Plan

Topic: Real Functions

Objectives & Outcomes

• Students will be able to define and identify real functions.
• Students will be able to graph real functions using a provided graph as a guide.

Materials

• Real functions worksheet
• Graph paper
• Calculator

Warm-up

• Ask students if they have ever taken a math class about functions before. If so, ask them to describe what a function is and what it is used for.
• Give students a brief overview of functions and their uses in everyday life.

Direct Instruction

• Begin by introducing the concept of real functions, and explain that they are functions that are defined on the real number line.
• Show students some examples of real functions, such as f(x) = x2 and f(x) = sin(x).
• Explain the properties of real functions, such as the fact that they are continuous, differentiable, and have unique extrema.
• Discuss the fact that the graph of a real function is a set of points that satisfy the function's equation, and can be plotted using a graphing calculator or software.

Guided Practice

• Divide the class into small groups and give each group a real function to work with.
• Have the students use their graphing calculators or software to plot the graph of the function.
• Have them identify the points where the function has a maximum or minimum, and explain their reasoning.
• Ask students to explain the properties of real functions that are demonstrated by the function they are working with.

Independent Practice

• Give each student a worksheet containing several real functions to graph and analyze.
• Have them use their graphing calculators or software to plot the graphs of the functions and identify any maxima or minima.
• Have them write a short paragraph explaining the properties of real functions that are demonstrated by the functions they have graphed.

Closure

• Review the key concepts of real functions, including the importance of conveying a relationship between input and output, and the different types of real functions.
• Ask students to share their findings from the independent practice and discuss how these relate to the concepts reviewed.

Assessment

• Observe students during the guided practice to assess their understanding of the concepts discussed.
• Collect and grade the functions written for the independent practice.
• Administer a quiz to assess students' understanding of real functions.