"Exponential Function" Exponential Function and Logarithmic Function PPT (Application of Exponential Function and Its Properties in Lesson 2)

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"Exponential Function" Exponential Function and Logarithmic Function PPT (Application of Exponential Function and Its Properties in Lesson 2)

Part One: Learning Objectives

Able to use the monotonicity of exponential functions to compare large and small problems related to exponentials

Ability to solve exponential equations and exponential inequalities using the monotonicity of exponential functions

Able to find the monotonicity of composite functions related to exponential functions

Will solve practical problems related to exponential functions

Exponential function PPT, part 2: interactive teaching and practice

Using the monotonicity of exponential functions to compare sizes

Compare the sizes of the following sets of numbers:

(1)1.52.5 and 1.53.2;

(2)0.6-1.2 and 0.6-1.5;

(3)1.70.2 and 0.92.1.

[Solution] (1) 1.52.5 and 1.53.2 can be regarded as two function values ​​of the function y=1.5x. Since the base 1.5>1,

So the function y=1.5x is an increasing function on R,

Because 2.5<3.2, so 1.52.5<1.53.2.

(2)0.6-1.2, 0.6-1.5 can be regarded as two function values ​​​​of the function y=0.6x,

Because 0<0.6<1,

So the function y=0.6x is a decreasing function on R,

Because -1.2>-1.5, so 0.6-1.2<0.6-1.5.

(3) From the properties of exponential functions, 1.70.2>1.70=1, 0.92.1<0.90=1,

So 1.70.2>0.92.1.

regular method

Compare the three types of power values ​​and their processing methods

Solve simple exponential equations and exponential inequalities

Find the value range of x that satisfies the following conditions.

(1)3x-1>9x;

(2)a-5x>ax+7 (a>0, and a≠1).

regular method

(1) The types of exponential equations can be divided into:

①The equation of the form af(x)=ag(x)(a>0, and a≠1) is solved as f(x)=g(x);

②For equations of the form a2x+b•ax+c=0 (a>0, and a≠1), use the element substitution method to solve it.

(2) The type of exponential inequality is af(x)>ag(x)(a>0, and a≠1).

①When a>1, f(x)>g(x);

②When 0

The general solution to inequalities containing exponential expressions: first convert both sides of the inequality into exponential expressions with the same base, then use the monotonicity of the exponential function to remove the base, and transform it into a familiar inequality solution.

Exponential function PPT, the third part: feedback on meeting standards

1. Which of the following is correct ()

A． 2.52.5>2.53B． 0.82<0.83

C. π2<π2 D. 0.90.3>0.90.5

2. If the function f(x)=(2a-1)x is a decreasing function on R, then the value range of the real number a is ()

A． (0,1) B. (1,+∞)

C.12,1 D． (-∞,1)

3. The monotonically increasing interval of function y=121-x is ()

A． (-∞, +∞) B. (0,+∞)

C. (1, +∞) D. (0,1)

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Update Time: 2024-10-03

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

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