Cho ba đồ thị A, B, và C. Các đường nét đứt là đường tiệm cận.
Đồ thị nào biểu diễn biểu thức sau đây:

$$\displaystyle\lim_{x\to 1^-}h(x)=+\infty$$?
Chọn tất cả đáp án đúng:
Chọn tất cả đáp án đúng:
(Đáp án A) Function h is graphed. The x-axis goes from negative 4 to 4. The graph consists of 3 curves. The first curve starts in quadrant 2 and moves upward toward a vertical asymptote at x = negative 2. The second curve moves upward away from the vertical asymptote at x = negative 2, then toward a vertical asymptote at x = 1. The third curve moves upward away from the vertical asymptote at x = 1, then toward a vertical asymptote at x = 4.
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$y$$
$$x$$
$$\blueD h$$

A
Function h is graphed. The x-axis goes from negative 4 to 4. The graph consists of 3 curves. The first curve starts in quadrant 2 and moves upward toward a vertical asymptote at x = negative 2. The second curve moves upward away from the vertical asymptote at x = negative 2, then toward a vertical asymptote at x = 1. The third curve moves upward away from the vertical asymptote at x = 1, then toward a vertical asymptote at x = 4.
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$y$$
$$x$$
$$\blueD h$$
(Đáp án B) Function h is graphed. The x-axis goes from negative 4 to 4. The graph consists of 2 curves. The first curve moves downward away from a horizontal asymptote at y = 1, then toward a vertical asymptote at x = 1. The second curve moves upward away from the vertical asymptote at x = 1, then toward the horizontal asymptote at y = 1.
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$y$$
$$x$$
$$\blueD h$$

B
Function h is graphed. The x-axis goes from negative 4 to 4. The graph consists of 2 curves. The first curve moves downward away from a horizontal asymptote at y = 1, then toward a vertical asymptote at x = 1. The second curve moves upward away from the vertical asymptote at x = 1, then toward the horizontal asymptote at y = 1.
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$y$$
$$x$$
$$\blueD h$$
(Đáp án C) Function h is graphed. The x-axis goes from negative 4 to 4. The graph consists of 3 curves. The first curve moves downward away from a horizontal asymptote at y = negative 1, then toward a vertical asymptote at x = negative 3. The second curve moves downward away from the vertical asymptote at x = negative 3 to about (negative 1, negative 0.8), then moves upward toward a vertical asymptote at x = 1. The third curve moves upward away from the vertical asymptote at x = 1, then toward the horizontal asymptote at y = negative 1.
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$y$$
$$x$$
$$\blueD h$$

C
Function h is graphed. The x-axis goes from negative 4 to 4. The graph consists of 3 curves. The first curve moves downward away from a horizontal asymptote at y = negative 1, then toward a vertical asymptote at x = negative 3. The second curve moves downward away from the vertical asymptote at x = negative 3 to about (negative 1, negative 0.8), then moves upward toward a vertical asymptote at x = 1. The third curve moves upward away from the vertical asymptote at x = 1, then toward the horizontal asymptote at y = negative 1.
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$y$$
$$x$$
$$\blueD h$$

Question

Cho ba đồ thị A, B, và C. Các đường nét đứt là đường tiệm cận.
Đồ thị nào biểu diễn biểu thức sau đây:
 
$$\displaystyle\lim_{x\to 1^-}h(x)=+\infty$$?
Chọn tất cả đáp án đúng:
Chọn tất cả đáp án đúng:
(Đáp án A)   Function h is graphed. The x-axis goes from negative 4 to 4. The graph consists of 3 curves. The first curve starts in quadrant 2 and moves upward toward a vertical asymptote at x = negative 2. The second curve moves upward away from the vertical asymptote at x = negative 2, then toward a vertical asymptote at x = 1. The third curve moves upward away from the vertical asymptote at x = 1, then toward a vertical asymptote at x = 4.
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$y$$
$$x$$
$$\blueD h$$

A
Function h is graphed. The x-axis goes from negative 4 to 4. The graph consists of 3 curves. The first curve starts in quadrant 2 and moves upward toward a vertical asymptote at x = negative 2. The second curve moves upward away from the vertical asymptote at x = negative 2, then toward a vertical asymptote at x = 1. The third curve moves upward away from the vertical asymptote at x = 1, then toward a vertical asymptote at x = 4.
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$y$$
$$x$$
$$\blueD h$$
(Đáp án B)   Function h is graphed. The x-axis goes from negative 4 to 4. The graph consists of 2 curves. The first curve moves downward away from a horizontal asymptote at y = 1, then toward a vertical asymptote at x = 1. The second curve moves upward away from the vertical asymptote at x = 1, then toward the horizontal asymptote at y = 1.
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$y$$
$$x$$
$$\blueD h$$

B
Function h is graphed. The x-axis goes from negative 4 to 4. The graph consists of 2 curves. The first curve moves downward away from a horizontal asymptote at y = 1, then toward a vertical asymptote at x = 1. The second curve moves upward away from the vertical asymptote at x = 1, then toward the horizontal asymptote at y = 1.
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$y$$
$$x$$
$$\blueD h$$
(Đáp án C)   Function h is graphed. The x-axis goes from negative 4 to 4. The graph consists of 3 curves. The first curve moves downward away from a horizontal asymptote at y = negative 1, then toward a vertical asymptote at x = negative 3. The second curve moves downward away from the vertical asymptote at x = negative 3 to about (negative 1, negative 0.8), then moves upward toward a vertical asymptote at x = 1. The third curve moves upward away from the vertical asymptote at x = 1, then toward the horizontal asymptote at y = negative 1.
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$y$$
$$x$$
$$\blueD h$$

C
Function h is graphed. The x-axis goes from negative 4 to 4. The graph consists of 3 curves. The first curve moves downward away from a horizontal asymptote at y = negative 1, then toward a vertical asymptote at x = negative 3. The second curve moves downward away from the vertical asymptote at x = negative 3 to about (negative 1, negative 0.8), then moves upward toward a vertical asymptote at x = 1. The third curve moves upward away from the vertical asymptote at x = 1, then toward the horizontal asymptote at y = negative 1.
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$\small{1}$$
$$\small{2}$$
$$\small{3}$$
$$\small{\llap{-}1}$$
$$\small{\llap{-}2}$$
$$\small{\llap{-}3}$$
$$y$$
$$x$$
$$\blueD h$$

Accepted Answer

Để xác định đồ thị nào biểu diễn biểu thức $\displaystyle\lim_{x\to 1^-}h(x)=+\infty$, chúng ta cần kiểm tra các đồ thị để xem khi $x$ tiến đến 1 từ bên trái (tức là $x < 1$), giá trị của $h(x)$ có tiến đến dương vô cùng hay không.

Đồ thị A:
- Đồ thị này có ba đoạn đường cong.
- Đoạn thứ hai của đồ thị tiến đến đường thẳng đứng (tiệm cận đứng) tại $x = 1$ từ bên trái.
- Khi $x$ tiến đến 1 từ bên trái, giá trị của $h(x)$ tiến đến dương vô cùng.

Do đó, đồ thị A thỏa mãn điều kiện $\displaystyle\lim_{x\to 1^-}h(x)=+\infty$.

Đồ thị B:
- Đồ thị này có hai đoạn đường cong.
- Đoạn thứ nhất của đồ thị tiến đến đường thẳng đứng (tiệm cận đứng) tại $x = 1$ từ bên trái.
- Khi $x$ tiến đến 1 từ bên trái, giá trị của $h(x)$ tiến đến âm vô cùng.

Do đó, đồ thị B không thỏa mãn điều kiện $\displaystyle\lim_{x\to 1^-}h(x)=+\infty$.

Đồ thị C:
- Đồ thị này có ba đoạn đường cong.
- Đoạn thứ hai của đồ thị tiến đến đường thẳng đứng (tiệm cận đứng) tại $x = 1$ từ bên trái.
- Khi $x$ tiến đến 1 từ bên trái, giá trị của $h(x)$ tiến đến âm vô cùng.

Do đó, đồ thị C không thỏa mãn điều kiện $\displaystyle\lim_{x\to 1^-}h(x)=+\infty$.

Kết luận:
Chỉ có đồ thị A thỏa mãn điều kiện $\displaystyle\lim_{x\to 1^-}h(x)=+\infty$.

Đáp án: A

Cho ba đồ thị A, B, và C. Các đường nét đứt là đường tiệm cận. Đồ thị nào biểu diễn biểu thức sau đây: ? Chọn tất cả đáp án đúng: Chọn tất cả đáp án đúng:...