| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | C |
C |
| deepseekr1 | The point \((3, 6)\) on \(y = g(x)\) implies \(g(3) = 6\). For \(h(x) = (g(x))^2\), substituting \(x = 3\) gives \(h(3) = (g(3))^2 = 6^2 = 36\). Thus, the point \((3, 36)\) must be on \(y = h(x)\). The sum of its coordinates is \(3 + 36 = 39\). **Answer:** C |
C |
| gpto1 | C | C |
| GPT-4o | To determine the point on the graph of \( y = h(x) \) given that \( h(x) = (g(x))^2 \) and the point \((3,6)\) is on the graph of \( y = g(x) \): 1. Since the point \((3,6)\) is on the graph of \( y = g(x) \), it means \( g(3) = 6 \). 2. Now, we need to find the corresponding point on the graph of \( y = h(x) \), where \( h(x) = (g(x))^2 \). 3. Therefore, \( h(3) = (g(3))^2 = 6^2 = 36 \). So, the point \((3, 36)\) must be on the graph of \( y = h(x) \). Finally, the sum of the coordinates of the point \((3, 36)\) is \( 3 + 36 = 39 \). Answer: C. |
C |
| llama3.1-70B-Instruct | ## Step 1: Understand the relationship between g(x) and h(x) The function h(x) is defined as the square of g(x), so h(x) = (g(x))^2. ## Step 2: Determine the value of g(3) Since the point (3,6) is on the graph of y = g(x), we know that g(3) = 6. ## Step 3: Calculate the value of h(3) Using the relationship between g(x) and h(x), we can calculate h(3) = (g(3))^2 = 6^2 = 36. ## Step 4: Identify the point on the graph of y = h(x) The point on the graph of y = h(x) is (3, 36). ## Step 5: Calculate the sum of the coordinates of the point The sum of the coordinates of the point (3, 36) is 3 + 36 = 39. The final answer is: $\boxed{39}$ |
C |
| llama3.1-405B-Instruct | C |
C |
| DeepSeek-Coder-V2 | C | C |
| Qwen2-72B-Instruct | C. 39 | C |
| baichuan4 | B | C |
| doubao | If the point $(3,6)$ is on the graph of $y=g(x)$, then for $h(x)=(g(x))^2$, when $x=3$, $h(3)=(g(3))^2=6^2=36$. So the point $(3,36)$ is on the graph of $y=h(x)$ and the sum of the coordinates is $3+36=39$. So the answer is C. |
C |
| minimax | Given that the point $(3,6)$ is on the graph of $y=g(x)$, we know that $g(3)=6$. Now, for the function $h(x)=(g(x))^2$, we want to find the point on the graph of $y=h(x)$ that corresponds to $x=3$. We substitute $x=3$ into $h(x)$: $h(3) = (g(3))^2 = 6^2 = 36$ Therefore, the point on the graph of $y=h(x)$ is $(3,36)$. The sum of the coordinates of this point is $3 + 36 = 39$. The correct answer is: C. 39 |
C |
| kimi | Given that the point $(3,6)$ is on the graph of $y=g(x)$, we know that $g(3) = 6$. Now, the function $h(x) = (g(x))^2$ is defined for all $x$. Therefore, we can find $h(3)$ by squaring the value of $g(3)$: $$h(3) = (g(3))^2 = 6^2 = 36.$$ So, the point $(3,36)$ must be on the graph of $y=h(x)$. The sum of the coordinates of this point is: $$3 + 36 = 39.$$ Answer: C. 39 |
C |
| wenxinyiyan | C Explanation: 1. Given that the point $(3,6)$ is on the graph of $y = g(x)$, we can say that $g(3) = 6$. 2. Next, we are told that $h(x) = (g(x))^2$ for all $x$. To find the corresponding point on the graph of $y = h(x)$ when $x = 3$, we need to evaluate $h(3)$. 3. Substituting $g(3) = 6$ into $h(x) = (g(x))^2$, we get: $h(3) = (g(3))^2 = 6^2 = 36$ 4. Therefore, the point $(3,36)$ is on the graph of $y = h(x)$. 5. The sum of the coordinates of this point is $3 + 36 = 39$. |
C |
| zhipu | To determine the point that must be on the graph of \( y = h(x) \), we start with the given information. The point \((3, 6)\) is on the graph of \( y = g(x) \). This means that \( g(3) = 6 \). Next, we consider the function \( h(x) = (g(x))^2 \). Substituting \( x = 3 \) into \( h(x) \), we get: \[ h(3) = (g(3))^2 = 6^2 = 36 \] Thus, the point \((3, 36)\) must be on the graph of \( y = h(x) \). Now, we need to find the sum of the coordinates of this point: \[ 3 + 36 = 39 \] Therefore, the correct answer is: C. 39 |
C |
| gpto1 | C | C |
| deepseekv3 | To solve this problem, let's follow the steps systematically. 1. **Given Information:** - The point \((3, 6)\) lies on the graph of \(y = g(x)\). This means that \(g(3) = 6\). - The function \(h(x)\) is defined as \(h(x) = (g(x))^2\). 2. **Find \(h(3)\):** - Substitute \(x = 3\) into the definition of \(h(x)\): \[ h(3) = (g(3))^2 = 6^2 = 36 \] - Therefore, the point \((3, 36)\) must lie on the graph of \(y = h(x)\). 3. **Calculate the Sum of the Coordinates:** - For the point \((3, 36)\), the sum of the coordinates is: \[ 3 + 36 = 39 \] 4. **Conclusion:** - The sum of the coordinates is \(39\). **Answer:** \(\boxed{C}\) |
C |