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"End of Chapter Review Lesson" Concept and Properties of Functions PPT
reminder to explore
[Example 1] (1) Find the domain of the function y=5-x+x-1-1x2-9.
(2) Fold the wire of length a into a rectangle, find the analytical formula of the rectangular area y with respect to the side length x, and write the domain of this function.
regular method
1. The analytical expression of the function has been 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.
Find the analytical expression of a function
[Example 2] (1) The function f(x) is an odd function on R. When x>0, f(x)=x+1, then the analytical formula of f(x) is ______.
(2) It is known that f1+xx=1+x2x2+1x, then the analytical formula of f(x) is ________.
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.
3Including f(x) and f(-x) or f(x) and f(1/x), use the method of solving the system of equations.
4. If you know the analytical formula of one interval and find the analytical formula of another interval, you can use the parity transfer method.
2. (1) It is known that f(x)-3f(-x)=2x-1, then f(x)=________.
(2) The quadratic function f(x)=ax2+bx+c(a, b∈R, a≠0) satisfies the conditions: ①When x∈R, the image of f(x) is symmetrical about the straight line x=-1; ②f( 1)=1; ③The minimum value of f(x) on R is 0. Find the analytical formula of function f(x).
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