Logarithmic function. Properties.

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.

After the lesson,students will know :

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.

As a result of the lesson,students will be able to do it :

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.

Assessment:

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.

Prior Knowledge:

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.
Equipment:
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.