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Authoritative PPT Summary
"Function" One-time function PPT
Part One: Learning Objectives
1. Master the concept and representation methods of functions. (emphasis)
2. Be able to find the value of a function and determine the value range of the independent variable. (difficulty)
Function PPT, part 2: importing new lessons
Observe and think
Life is full of variables. Do you understand the relationship between these variables?
It records the daily price changes of a certain stock since its listing.
What is recorded is the electrical changes that occur in the heart's own bioelectricity during each cardiac cycle.
Function PPT, the third part: teaching new lessons
The concept and representation of functions
Scenario 1
Think about it, if you are sitting on a Ferris wheel, how does your height above the ground change over time?
The following figure reflects the relationship between the height h (m) of a point on the Ferris wheel and the rotation time t (min).
(1) Fill in the form according to the picture on the left:
(2) For a given time t, is the corresponding height h determined?
Scenario 2
the only y value
For any given layer number n, is the corresponding total number of objects y determined? How many y values correspond to it?
Cylindrical objects such as bottles or cans are often stacked as shown below. As the number of layers increases, how does the total number of objects change?
Scenario 3
When the volume of a certain mass of gas remains constant, if the temperature drops to -273°C, the pressure of the gas is zero. Therefore, physics regards -273°C as the zero degree of thermodynamic temperature. The thermodynamic temperature T (K) is related to the Celsius temperature t ( ℃) have the following quantitative relationship: T=t+273, T≥0.
(1) When t is equal to -43, -27, 0, and 18 respectively, what is the corresponding thermodynamic temperature T?
(2) Given any Celsius temperature t value greater than -273 ℃, is the corresponding thermodynamic temperature T determined? How many T values correspond to it?
In conclusion
function
Generally, if there are two variables x and y in a change process, and for each value of variable x, variable y has a unique value corresponding to it, then we say y is a function of x, where x is the self- variable.
Note: A function is not a number, it refers to the relationship between two variables in a certain change process.
The value range of the independent variable
Question: Among the above three questions, what values can the independent variables take to make the function meaningful?
Scenario 1
The value range of the independent variable t:__________
Scenario 2
Cylindrical objects such as cans are often stacked as shown below. As the number of layers increases, how does the total number of objects change?
The value range of the independent variable n: _________.
Scenario 3
When the volume of a certain mass of gas remains constant, if the temperature drops to -273°C, the pressure of the gas is zero. Therefore, physics regards -273°C as the zero degree of thermodynamic temperature. The thermodynamic temperature T (K) is related to the Celsius temperature t ( ℃) have the following quantitative relationship: T=t+273, T≥0.
The value range of the independent variable t:___________.
Function PPT, Part 4: Practice in class
1. Assume the distance is s, the time is t, and the speed is v. When v=60, the relationship between distance and time is ______. In this relationship, ______ is a constant, ______ is a variable, and ______ is _ _____The function.
2. There is 30kg of oil in the tank. The oil flows out from the pipe at a constant speed. After 1 hour, the functional relationship between the remaining oil quantity Q (kg) in the tank and the outflow time t (min) is ______, and the independent variable t is The value range is______.
3. Which of the following expressions does not mean that y is a function of x ( )
4. Xiao Ming’s father went for a walk in the morning. He walked 20 minutes from home to a park 800 meters away from home. He rested in the park for 10 minutes, and then returned home in 30 minutes. Then the distance between Xiao Ming’s father and home is s ( The functional relationship graph between unit: m) and the time away from home t (unit: min) is roughly ( )
5. Find the value range of the independent variable x in the following functions:
6. The charging standard for taxis in our city during the day is as follows: if the distance traveled does not exceed 3 kilometers, the fee will be 8 yuan; if it exceeds 3 kilometers, an additional 1.8 yuan will be charged for each kilometer for the distance exceeding 3 kilometers; assuming that the distance traveled by taxi is x (km) (x is an integer), the corresponding charge is y (yuan).
(1) Please write down the relationship between y and x when 03 respectively, and directly write the corresponding y values when x=2 and x=6;
(2) When 03, is y a function of x? Why?
Function PPT, Part 5: Class Summary
Definition: independent variable, dependent variable, constant
Relational expressions of functions: three representation methods
The value range of the independent variable
function value
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