"Parity of Functions" Concept and Properties of Functions PPT (Application of Parity of Functions in Lesson 2)

Description

"Parity of Functions" Concept and Properties of Functions PPT (Application of Parity of Functions in Lesson 2)

Part One: Learning Objectives

Can use the parity and evenness of functions to find the analytical formula of the function

Able to use the monotonicity and parity of functions to solve comprehensive problems such as comparing sizes, finding optimal values, and solving inequalities.

Parity of functions PPT, part 2: interactive lecture and practice

Use parity and evenness to find the analytical expression of a function

If the function f(x) is an odd function defined on R, when x>0, f(x)=x2-2x-1, find the analytical formula of the function f(x).

Interactive exploration

1. (Various question method) Under the conditions of this example, find the value of f(-3).

2. (Variable conditions) Change the "odd function" in this example to an "even function", and other conditions remain unchanged. Find the analytical formula of the function f(x) when x<0.

regular method

The idea of ​​using parity and evenness to find the analytical expression of a function

(1) "Set whomever you ask for", that is, in which interval you find the analytical formula, x will be set in that interval.

(2) Use the analytical expression of the known interval to substitute.

(3) Use the parity of f(x) to write -f(x) or f(-x), thereby solving f(x).

Comprehensive problem of parity and monotonicity of functions

Angle 1: Comparing size issues

Suppose the domain of the even function f(x) is R. When x∈[0,+∞), f(x) is an increasing function, then f(-2), f(π), f(- The size relationship of 3) is ()

A． f(π)>f(-3)>f(-2)

B． f(π)>f(-2)>f(-3)

C. f(π)

D. f(π)

Angle 2 Solving Inequalities

It is known that the function f(x)=xx2+1 defined on (-1,1).

(1) Try to judge the parity and monotonicity of f(x) on (-1, 1);

(2) Solve the inequality f(t-1)+f(2t)<0.

regular method

Two types of parity and monotonicity comprehensive problems

(1) Compare size

① When the independent variables are in the same monotonic interval, the monotonicity of the function is directly used to compare the magnitude;

② If the independent variables are not in the same monotonic interval, the parity of the function needs to be used to transform the independent variables into the same monotonic interval, and then the monotonicity is used to compare the sizes.

(2) Solve the inequality

①Use the known conditions and combine the parity of the function to transform the known inequality into the form of f(x1)＜f(x2) or f(x1)＞f(x2);

②According to the fact that the monotonicity of odd functions on the symmetric interval is the same, and the monotonicity of the even function on the symmetric interval is opposite, take off the "f" in the inequality and convert it into a simple inequality (group) to solve.

Parity of functions PPT, the third part: feedback on compliance

1. Among the following functions, the function that is both an even function and monotonically increasing on (0, +∞) is ()

A． y＝x3　B． y＝|x|＋1

C. y=-x2+1 D. y=-2x

2. If the odd function f(x) is a decreasing function on the interval [1,5], and the minimum value is 3, then f(x) is on the interval [-5,-1] yes()

A． Increasing function with minimum value 3

B． Increasing function with a maximum value of 3

C. Decreasing function and the minimum value is -3

D. Decreasing function and the maximum value is -3

3. Assume that the odd function f(x) is a decreasing function on (0, +∞), and f(1)=0, then the solution set of the inequality f(x)-f(-x)x<0 is ()

A． (-1,0)∪(1,+∞)

B． (-∞,-1)∪(0,1)

C. (-∞,-1)∪(1,+∞)

D. (-1,0)∪(0,1)

4. It is known that the function f(x) is an odd function defined on R, and it is a decreasing function. If the real numbers a and b satisfy f(a)+f(b)>0, then a+b_______0 (fill in ">" "<" or "＝")．

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For more information about the PPT courseware "The Concept and Properties of Functions, Parity and Evenness of Functions, and Applications of Parity of Functions", please click the "Concepts and Properties of Functions ppt Parity of Functions ppt Applications of Parity of Functions" ppt tag.

"Parity of Functions" Concept and Properties of Functions PPT (Application of Parity in Lesson 2):

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"Parity of Functions" Concept and Properties of Functions PPT (Application of Parity in Lesson 2):

"Parity of Functions" Concept and Properties of Functions PPT (Application of Parity in Lesson 2) Part One: Learning Objectives 1. Be able to find function values ​​or analytical expressions based on parity of functions. 2. Able to use the parity and monotonicity of functions to analyze and solve simpler problems..

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Update Time: 2024-11-10

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

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