Listen to each assistant's responses to the following instruction, and give each a score out of 100 and an explanation for the score. Here are some additional guidelines: * Do not award bonus points. * If the instruction includes additional context from which the response should be generated, deduct points if the response includes details not found within the provided context. * The assistants should not be making assumptions about the intent of the question. * If the instruction asks for results in a specific format, e.g. JSON, 50% of the score should be whether or not the assistant produced the correct format. * Award points for effort and problem formulation when the instruction is related to solving mathematical equations or coding. Respond in format "[assistant number]. [score]/100 - [explanation] Instruction: Given that h(x) = 2x^3 + 4x^2 - 6x + 1, find the value of h(-1). Assistant 1's response: To find the value of h(-1), we must first rewrite the function with x=-1: h(-1) = 2(-1)^3 + 4(-1)^2 - 6(-1) + 1 h(-1) = -8 + 4 - 6 + 1 h(-1) = -1 Assistant 2's response: To find the value of h(-1), you need to substitute -1 in place of x: h(-1) = 2(-1)^3 + 4(-1)^2 - 6(-1) + 1 The first term simplifies to -2 (because -1 cubed is -1 times itself twice, which is -1 x -1 x -1 = -1) The second term simplifies to 4 (because -1 squared is 1) The third term simplifies to 6 (because -1 multiplied by -6 is 6) So, h(-1) = -2 + 4 + 6 + 1 = 9 Assistant 3's response: To find the value of h(-1), we can substitute -1 for x in the equation h(x) = 2x^3 + 4x^2 - 6x + 1. This gives us: h(-1) = 2(-1)^3 + 4(-1)^2 - 6(-1) + 1 = -8 + 4 + 6 + 1 = 0 Therefore, the value of h(-1) is 0. Assistant 4's response: To find the value of h(-1), we can substitute -1 for x in the given function h(x). h(-1) = 2(-1)^3 + 4(-1)^2 - 6(-1) + 1 h(-1) = 2(-1) + 4(-1) - 6 + 1 h(-1) = -1 - 4 + 5 h(-1) = -12 Therefore, the value of h(-1) is -12. Assistant 5's response: To find the value of h(x) at x = -1, we simply replace x with -1 in the formula for h(x): h(-1) = 2(-1)^3 + 4(-1)^2 - 6(-1) + 1 h(-1) = -2 + 4 - 6 - 1 h(-1) = -13 Therefore, the value of h(x) at x = -1 is -13. Assistant 6's response: To find the value of h(-1), we need to substitute -1 for x in the given expression for h(x). h(-1) = 2(-1)^3 + 4(-1)^2 - 6(-1) + 1 h(-1) = -8 + 4 - 6 + 1 h(-1) = -1 Therefore, h(-1) = -1.
1. 100/100 - The assistant correctly substituted the value of x as -1 in the given function and calculated the correct result, h(-1) = -1.
2. 0/100 - The assistant made a mistake in calculating the first term (-8 instead of -2), leading to an incorrect answer for h(-1).
3. 0/100 - The assistant made a mistake in calculating the first term (-8 instead of -2), leading to an incorrect answer for h(-1).
4. 0/100 - The assistant made mistakes in calculating the second and third terms (incorrectly using -1 instead of 1 and -6 instead of 6), leading to an incorrect answer for h(-1).
5. 0/100 - The assistant made a mistake in calculating the third term (-6 instead of 6), leading to an incorrect answer for h(-1).
6. 100/100 - The assistant correctly substituted the value of x as -1 in the given function and calculated the correct result, h(-1) = -1.