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Khái niệm hàm số

Hàm số là gì? Có những cách cho hàm số nào? Giá trị của hàm số là gì?
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1. Lý thuyết

- Khái niệm hàm số: Nếu đại lượng \(y\) phụ thuộc vào đại lượng thay đổi \(x\) sao cho với mỗi giá trị của \(x\) ta luôn xác định được chỉ một giá trị tương ứng của \(y\) thì \(y\) được gọi là hàm số của \(x\) và \(x\) gọi là biến số.

- Cách cho một hàm số:

+ Nếu \(x\) thay đổi mà \(y\) không đổi thì \(y\) gọi là hàm hằng.

+ Hàm số có thể được cho bằng bảng, bằng công thức.

+ Khi \(y\) là hàm số của \(x\) ta có thể viết \(y = f(x),\,\,y = g(x),....\,\,\)

- Giá trị của hàm số: Cho hàm số y = f(x) xác định tại x = a. Giá trị tương ứng của hàm số f(x) khi x = a được gọi là giá trị của hàm số y = f(x) tại x = a, kí hiệu f (a).

Bảng giá trị của hàm số y = f(x)

x a b c ... ...
y = f(x) f(a) f(b) f(c) ... ...
 

2. Ví dụ minh họa

Ví dụ về Hàm số♈: Ta có bảng nhiệt độ dự báo ở Thủ đô Hà Nội ngày 25/5/2023.

t(h) 10 11 12 13

T(0C)

 32 33 34 34
Ta có nhiệt độ T là hàm số của thời điểm t vì mỗi giá trị của t chỉ xác định đúng một giá trị của T.

Ngược lại, thời điểm t không phải là hàm số của nhiệt độ T, vì nhiệt độ T = 340ℱC tương ứng với hai thời điểm khác nhau t = 12 và t = 13.

Ví dụ Giá trị của hàm số: Cho hàm số y = f(x) = x + 3.

f(-2) = -2 + 3 = 1;                    f(0) = 0 + 3 = 3

Ví dụ Giá trị của hàm số: Cho hàm số y = f(x) = -2x + 1.

a. Tính f(10); f(-10)b. Lập bảng giá trị của hàm số với x lần lượt bằng -2; -1; 0; 1; 2

Giải

a. f(10) = -2.10 + 1 = -20 + 1 = -19    f(-10) = -2.(-10) + 1 = 20 + 1 = 21b. Bảng giá trị của hàm số với x lần lượt bằng -2; -1; 0; 1; 2 là:
x -2 -1 0 1 2
y = f(x) = -2x + 1 5 3 1 -1 -3

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