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Authoritative PPT Summary
"Function" PPT courseware
Part One: Learning Objectives
1. Can list the relational expressions of functions.
2. Able to find the value range of independent variables and the value of functions.
Key points:
Find the value range of the independent variable
difficulty:
Find the value range of the independent variable
Knowledge review
1. Definition of function
Generally, in a certain change process, there are two variables x, y. If for every certain value of x, y has a unique certain value, then y is said to be a function of x.
2. What are the representation methods of functions?
Analytical method List method Image method
Function PPT, part 2: give it a try
When x takes on what value, the following functional expressions make sense?
1. y＝３x＋1
X takes all real numbers
2. y=4/x-2
∵x-2≠0
∴x≠2
3.y＝√x-4
∵X-4≥0
∴X≥4
4. On Children’s Day, each person is given 2 candies. The functional relationship between the total number of people x and the total number of candies y is ________, where the value range of the number of people x is __________
Function PPT, the third part: knowledge accumulation
When finding the analytical expression of a function, you can first obtain the equation between the function and the independent variables, and then solve the analytical expression of the function with respect to the independent variables.
When finding the value range of a function’s independent variable, two aspects should be considered:
①The algebraic expression must be meaningful ②Consistent with reality
Three basic types of questions about functions:
① Find the analytical formula
② Find the value range of the independent variable
③If the value of the independent variable is known, find the corresponding function value or if the function value is known, find the value of the corresponding independent variable.
Function PPT, part 4: show off your skills
1. Suppose the angle of the vertex of an isosceles triangle is y and the angle of the base is x, then ( )
(A) y=180-2x (x can be all real numbers)
(B) y＝180-2x（0≤x≤90）
(C) y＝180－2x (0＜x＜90)
(D) y=180-1/2x (0�x�90)
2. If the outer diameter of a cylindrical water pipe is R and the inner diameter is 6, the functional relationship between its cross-sectional area S and the outer diameter R is S = π (R2-36), then the value range of R is ( )
(A) All real numbers (B) All positive real numbers
(C) All non-negative real numbers (D) All real numbers greater than 6
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