Làm thế nào để duy trì giao tiếp xã hội cho người cần chăm sóc
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a/an is a person who needs others to take care of
- NhữngConsider the function $f(x) = x^2 + 2x - 3$. What is the range of this function when the domain is restricted to $x \ge -2$? The function is given by $f(x) = x^2 + 2x - 3$. This is a quadratic function, and its graph is a parabola opening upwards because the coefficient of the $x^2$ term is positive (1 > 0). To find the vertex of the parabola, we can use the formula for the x-coordinate of the vertex $x_v = -\frac{b}{2a}$. In this function, $a = 1$ and $b = 2$, so $x_v = -\frac{2}{2(1)} = -\frac{2}{2} = -1$. Now, we can find the y-coordinate of the vertex by substituting $x_v$ back into the function $y_v = f(-1) = (-1)^2 + 2(-1) - 3 = 1 - 2 - 3 = -4$. So, the vertex of the parabola is at the point $(-1, -4)$. The domain of the function is restricted to $x \ge -2$. Since the parabola opens upwards, the minimum value of the function will occur at the vertex if the x-coordinate of the vertex is within the given domain. In this case, $x_v = -1$, and since $-1 \ge -2$, the vertex is within the restricted domain. The minimum value of the function within the restricted domain is the y-coordinate of the vertex, which is $-4$. Now we need to consider the behavior of the function as $x$ increases within the domain $x \ge -2$. Since the parabola opens upwards and the vertex is at $x = -1$, the function will increase for values of $x$ greater than $-1$. To find the upper bound of the range (if any), we need to examine the behavior of the function as $x$ goes towards infinity within the restricted domain. As $x \to \infty$, $f(x) = x^2 + 2x - 3 \to \infty$. Alternatively, we can evaluate the function at the boundary of the restricted domain, $x = -2$ $f(-2) = (-2)^2 + 2(-2) - 3 = 4 - 4 - 3 = -3$. Since the minimum value of the function within the domain $x \ge -2$ is $-4$ (at $x = -1$) and the function increases for $x > -1$, the range of the function for $x \ge -2$ will be all values greater than or equal to the minimum value. Therefore, the range of the function $f(x) = x^2 + 2x - 3$ when the domain is restricted to $x \ge -2$ is $[-4, \infty)$. Final Answer The final answer is $\boxed{[-4, \infty)}$
- Làm thế nào để giải quyết các tranh chấp pháp lý liên quan đến việc chăm sóc
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- Vai trò của tình nguyện viên trong việc hỗ trợ người cần chăm sóc là gì
- Những lưu ý về văn hóa trong việc chăm sóc người lớn tuổi tại Việt Nam
- Làm thế nào để lập kế hoạch chăm sóc toàn diện
- Tiêu chuẩn chất lượng cho các cơ sở chăm sóc người cần chăm sóc là gì
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