"Logarithmic Function" Exponential function and logarithmic function PPT (the concept, image and properties of logarithmic function in the first lesson)

Description

"Logarithmic Function" Exponential function and logarithmic function PPT (the concept, image and properties of logarithmic function in the first lesson)

Part One: Learning Objectives

Understand the concept of logarithmic functions and be able to judge logarithmic functions

Preliminarily grasp the image and properties of logarithmic functions

Able to use the properties of logarithmic functions to solve domain problems related to them

Exponential function and logarithmic function PPT, part 2 content: independent learning

Problem guide

Preview the textbook P130-P135 and think about the following questions:

1. What is the concept of logarithmic function? What are the characteristics of its analytical formula?

2. What is the shape of the graph of a logarithmic function? Can you draw the graph of y=log2x and y=log12x?

3. What properties of the function can you observe by looking at the graph of a logarithmic function?

A preliminary exploration of new knowledge

1. The concept of logarithmic function

Generally, the function y=____________________ is called a logarithmic function, where ____ is the independent variable and the domain of the function is __________.

■Instructions from famous teachers

In the definition expression of logarithmic function y=logax (a>0, and a≠1), the coefficient in front of logax must be 1, and the independent variable x is in the position of a real number, otherwise it is not a logarithmic function.

2. Graph and properties of logarithmic function

■Instructions from famous teachers

The relationship between the base a and 1 determines the "rise and fall" of the image of the logarithmic function: when a>1, the image of the logarithmic function "rises"; when 0

3. Inverse function

The exponential function y=ax (a>0, and a≠1) and the logarithmic function y=logax (a>0, and a≠1) are inverse functions of each other. The _______ and _______ of the two are exactly interchangeable.

self-test

Judge whether it is true or false (mark “√” if it is correct and “×” if it is wrong)

(1)y=log2x2 and y=logx3 are both logarithmic functions. ()

(2) The domain and value range of the logarithmic function are both R.()

(3) The graph of the logarithmic function must be on the right side of the y-axis. ()

(4) The functions y=log2x and y=2x are inverse functions of each other. ()

Which of the following functions is a logarithmic function ()

A． y＝lnx B． y=ln(x+1)

C. y＝logxe D． y＝logxx

The domain of function f(x)=lg(3x)-2-x is ()

A． (0,2) B. [0,2]

C. [0,2) D． (0,2]

Exponential function and logarithmic function PPT, the third part of the content: interactive teaching and practice

The concept of logarithmic function

Which of the following functions are logarithmic functions?

(1)y=logax(a>0, and a≠1);

(2)y=log2x+2;

(3)y=8log2(x+1);

(4)y=logx6 (x>0, and x≠1);

(5)y=log6x.

[Solution] The real number in (1) is not the independent variable x, nor the logarithmic function. In (2), 2 is added after the logarithmic expression, so it is not a logarithmic function. The real number in (3) is x+1, not x, and the coefficient is not 1, so it is not a logarithmic function. (4) The base number is the independent variable x, not a constant, so it is not a logarithmic function. (5) The base number is 6, the real number is x, and the coefficient is 1, which conforms to the definition of a logarithmic function, so it is a logarithmic function.

Domain issues related to logarithmic functions

Find the domain of the following functions:

(1)y=1log2(x-1);

(2)y=log2(16-4x);

(3)y=log(x-1)(3-x)．

regular method

(1) Principles to be followed when finding the domain of functions related to logarithmic functions

①The denominator cannot be 0;

②When the root exponent is an even number, the radicand is non-negative;

③The true number of logarithm is greater than 0, and the base is greater than 0 and not 1.

(2) Steps to find the domain of a function

① List the inequalities (groups) that make the function meaningful;

② Simplify and solve the value range of the independent variables;

③Determine the domain of the function.

Exponential function and logarithmic function PPT, Part 4: Feedback on achievement of standards

1. The graph of the logarithmic function passes through the point M (16, 4), then the analytical formula of this logarithmic function is ()

A． y=log4xB． y＝log14x

C. y＝log12x D． y=log2x

Analysis: Choose D. Since the graph of the logarithmic function passes through the point M (16, 4), 4 = loga16, and a = 2. Therefore, the analytical formula of the logarithmic function is y = log2x, so choose D.

2. It is known that the graph of the function f(x)=loga(x-1)+4(a>0, and a≠1) always passes through the fixed point Q, then the coordinates of the Q point are ()

A． (0,5)B. (1,4) C. (2,4) D. (2,5)

3. If the graph of function y=loga(x+a)(a>0 and a≠1) passes through the point (-1, 0).

(1) Find the value of a;

(2) Find the domain of the function.

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Update Time: 2024-07-11

This template belongs to Mathematics courseware People's Education High School Mathematics Edition A Compulsory Course 1 industry PPT template

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