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

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

Part One: Learning Objectives

1. Master the properties of exponential functions and be able to apply them, and be able to use the monotonicity of exponential functions to compare powers and solve inequalities. (emphasis)

2. Through studying the content of this section, you can further understand that function graph is an important tool for studying functions, and be able to use exponential functions to study some practical problems. (difficulty)

core competencies

Cultivate logical reasoning and mathematical operation literacy with the help of the properties and applications of exponential functions.

Exponential function PPT, part 2: cooperative exploration to improve literacy

Using the monotonicity of exponential functions to compare sizes

[Example 1] Compare the sizes of the following groups 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;

(4) a1.1 and a0.3 (a>0 and a≠1).

[ Solution function, 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 function y=0.6x,

Because the function y=0.6x is a decreasing function in R,

And -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.

(4) When a>1, y=ax is an increasing function on R, so a1.1>a0.3;

When 0

regular method

How to compare powers

1Construct an exponential function when comparing powers with the same base, and compare based on their monotonicity.

2. When the exponents have the same base but different bases, draw the graph of the exponential function with the base of the two powers as the base respectively. When x takes the same power as the exponent, the size of the function value can be observed.

3. When the base and exponent are different, use the power that is the same as one of the bases and the same exponent of the other to compare the two numbers, or use "1" to compare the two numbers.

4. When the base number contains parameters, the discussion should be classified and discussed according to the two situations of base number a>1 and 0

Class summary

1. The main way to compare the magnitude of two exponential values

(1) To compare the sizes of shapes such as am and an, the monotonicity of the exponential function y=ax can be used.

(2) Comparing the sizes of am and bn, generally find an "intermediate value c". If amc and c>bn, then am>bn.

2. Points to note when solving simple exponential inequalities

(1) Inequalities of the form ax>ay can be solved with the help of the monotonicity of y=ax. If the value of a is uncertain, it needs to be discussed in two cases: 01.

(2) For inequalities of the form ax>b, pay attention to convert b into an exponential power with a as the base, and then solve it with the help of the monotonicity of y=ax.

(3) Inequalities of the form ax>bx can be solved with the help of images.

3. (1) When studying the monotonic interval of type y=af(x), we should pay attention to whether a>1 or 0

When a>1, y=af(x) and f(x) are monotonic.

When 0

(2) When studying a monotonic interval of type y=f(ax), it is necessary to pay attention to whether ax is an increasing or decreasing interval of f(u).

Exponential function PPT, the third part: reaching the standard in class and solidifying the double base

1. Thinking and analysis

(1)y=21-x is an increasing function on R. ()

(2) If 0.1a>0.1b, then a>b.()

(3) a and b are both greater than 0 and not equal to 1. If ax=bx, then x=0.()

(4) Since y=ax (a>0 and a≠1) is neither an odd function nor an even function, the exponential function and other functions cannot form a function with odd and even properties. ()

2. If 2x+1<1, then the value range of x is ()

A． (-1,1)

B． (-1, +∞)

C. (0,1)∪(1,+∞)

D. (-∞,-1)

3. Which of the following is correct ()

A． 1.72.5>1.73

B． 0.82＜0.83

C. π2＜π2

D. 0.90.3>0.90.5

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