"Primary Function" PPT Courseware 4

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"Primary Function" PPT Courseware 4

What is a function?

In a certain change process, there are two variables x and y. If an x ​​value is given, a y value is determined accordingly, then we call y a function of x, where x is the independent variable and y is the dependent variable.

Let’s discuss the two functional relationships:

(1)y=0.5x+3 (2) y=-0.2x+100

What is the relationship between structural characteristics?

1. is an equation containing two variables x, y;

2. The exponents of the independent variable x and the dependent variable y are both linear;

3. The coefficient of the independent variable x is not 0.

If the relationship between two variables x and y can be expressed in the form of y=kx+b (k, b are constants, k≠0), then y is said to be a linear function of x. (x is the independent variable, y is the dependent variable)

When b=0, it is said that y=kx is a proportional function of x

The function is a linear function. The analytical formula is: y=kx+b (k, b are constants, k≠0)

The function is a proportional function and the analytical formula is: y=kx (k≠0)

Write the relationship between y and x in each of the following questions, and judge: Is y a linear function of x? Is it a proportional function?

(1) The car is traveling at a constant speed of 60 kilometers/hour, and the relationship between the driving distance is y (kilometers) and the driving time x (hours);

(2) The relationship between the area y (c m2) of a circle and its radius x (cm);

(3) A tree is now 50 cm tall and grows 2 cm taller every month. The height of the tree will be y cm after x months.

Solution: (1) y=60x, y is a linear function of x and a proportional function of x.

(2) y= πx², y is not a proportional function of x, nor is it a linear function of x.

(3) y=2x + 50, y is a linear function of x, but not a proportional function of x.

A bookstore offers two ways to rent books: one is for renting books on a sporadic basis, charging 1 yuan per book, and the other is charging for a membership card, which costs 12 yuan per month and rents books for 0.4 yuan per book. Xiaobin often comes to the store to rent books. Books, if the number of books rented per month is x.

(1) Write the functional relationship between the amount y1 (yuan) payable for sporadic book rental and the number of books rented x (book).

(2) Write the functional relationship between the amount y2 (yuan) payable by the membership card rental method and the number of books rented x (books).

(3) Which method of renting books should Xiaobin choose to be more cost-effective? Why?

Simple explanation: (1) y1=x

(2) y2=0.4x+12

(3) From x=0.4x+12, it is cost-effective when x>20.

Keywords: One-time function courseware, Beijing Normal University edition eighth-grade mathematics volume PPT courseware, eighth-grade mathematics slide courseware download, one-time function PPT courseware download, .ppt format

For more information about the "Linear Function" PPT courseware, please click the "Linear Function PPT" tab.

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Update Time: 2024-09-07

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