Logarithmic function. Properties.
- Author:
- cracana dumitru, Judith
This book contains the lesson project that introduces the logarithmic function and discovers the properties of this function.
- Subject: Mathematics
- Grade Level: 10th grade
- Duration: about 50 min
- Technology setting: Computer and projector for teacher, computers/ tablets for students.
Topic.
Logarithmic function. Properties.
The geometric representation of the graph of the logarithmic base function supraunitary and subunitary, identification of its inversion by right symmetry y = x (first bisector), solving some equations.
Learning Outcomes
During the lesson, students:
- will discover the graph of the logarithmic function with a supraunit and subunit base;
- will see, through graphical reading, the properties of the functions: monotony, convexity, infinite variation (slope) ...
- will explore the sign of the logarithmic function;
- will identify the exponential function as the inverse logarithmic function.
- the properties of the logarithmic function in relation to the base;
- students will know how to compare the logarithm of the same number in relation to the base;
- that the logarithmic function is inverse to the exponential function.
- to plot the logarithmic function graph;
- to compare two logarithms;
- to resolve some of the equations graphically.
Lesson Objectives and Assessment
Lesson objectives:
- students can draw through points the graph of the logarithmic function;
- students can explain the properties of the logarithmic function;
- in relation to the base, can distinguish the differences between properties;
- identifies the inverse logarithmic function;
- can explain inequalities between logarithms;
- can read from the graph the sign of the logarithmic function.
- check the students' written notes;
- in applet 2, changing the logarithm base, students are required to observe the properties and list them;
- discussions about the power of infinite convergence of the logarithm with the help of the tangent slope to the graph.
- students need to be familiar with identifying the properties of a graphical reading function;
- students need to know the graph of the exponential function;
- students need to know the relationship between the function graphs and .
Teaching Strategies
Methods and strategies:
- learning by discovery;
- questioning;
- conversation, observation.
- Computer and projector for teacher;
- computers/ tablets for students.
Technology Integration
- Students need to be familiar with identifying the properties of a graphical reading function; to know the graph of the exponential function; to know the relationship between the function graphs and .
- In order to have no problems, before the lesson I will ensure that all pupils have their applets downloaded on their equipment.