"End of Chapter Review and Improvement Course" Concept and Properties of Functions PPT

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"End of Chapter Review and Improvement Course" Concept and Properties of Functions PPT

Comprehensive improvement

Function domain and range

(1) The domain of function f(x)=3x21-x+(3x-1)0 is ()

A.－∞,13

B.13,1

C.-13,13

D.－∞，13∪13，1

(2) It is known that the domain of function y=f(x+1) is [-2,3], then the domain of y=f(2x-1) is ()

A.0,52B． [-1,4]

C. [-5,5] D. [-3,7]

(3) Find the value range of the following functions:

①y=2x+1x-3;

②y=x+41-x;

③y＝1x-2x, x∈-2,-12.

regular method

Find the type and method of function domain

(1) The analytical expression of the function is given: the domain of the function is the set of values ​​of the independent variables that make the analytical expression meaningful.

(2) Practical problems: To find the domain of a function, we should not only consider the meaningful analytical expression, but also consider making the practical problem meaningful.

(3) Composite function problem:

①If the domain of f(x) is [a,b], the domain of f(g(x)) should be solved by a≤g(x)≤b;

②If the domain of f(g(x)) is [a, b], then the domain of f(x) is g(x) on [a, b] range.

[Note] (1) x in f(x) has the same status as g(x) in f(g(x)).

(2) The domain of definition always refers to the scope of the independent variable.

Track training

1. Suppose the domain of function f(x) is [1,5], then the domain of function f(2x-3) is ()

A． [2,4] B. [3,11]

C. [3,7] D. [1,5]

2. Assume that the value range of function f(x)=-2x2+4x in the interval [m,n] is [-6,2], then the value range of m+n is ________.

analytic expression of function

(1) It is known that f(x+1)=x2-5x+4, then f(x)=________.

(2) It is known that the function f(x) is an odd function defined on R. When x>0, f(x)=x2-2x+3.

① Find the analytical formula of function f(x) on R;

②Write the monotonic interval of the function (just write it, no proof is required).

regular method

Question types and corresponding solutions for finding analytical expressions of functions

(1) Given the analytical formula of the form f(g(x)), find the analytical formula of f(x) using the substitution method or matching method.

(2) If the type of function is known (often a linear function or a quadratic function), use the undetermined coefficient method.

(3) Including f(x) and f(-x) or f(x) and f1x, use the method of solving the system of equations.

(4) If the analytical formula of one interval is known, the parity transfer method can be used to find the analytical formula of another interval.

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Update Time: 2024-09-08

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

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