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{ "quality": "incomplete", "question_count": 5, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Function Identification", "Function Evaluation", "One-to-One Functions" ], "current_concepts": [ "Function Identification", "Function Evaluation", "One-to-One Functions" ] } ## Determine if the relations are functions $$ \begin{aligned} &\text{For 1: } y = 2x + 8 \text{ is a linear equation. Each input } x \text{ yields exactly one output } y. \implies \text{Function} \ &\text{For 2: } \{(2,1), (3,2), (-1,1), (0,-2)\}. \text{ Each } x\text{-value } \{2, 3, -1, 0\} \text{ is unique.} \implies \text{Function} \end{aligned} $$ ## Evaluate the function $$ \begin{aligned} &\text{The function is cut off, but standard context for this exercise set is } f(x) = -3x - 1 \text{ or similar.}\ &\text{However, since the formula for } f(x) \text{ is cut off at the edge of the image, we can only solve what is fully visible.}\ &\text{We will evaluate } f(x) = -2(x-1)^2 + 3 \text{ from exercise 5 as a reference, or state it is incomplete.} \end{aligned} $$ ## Show the function is not one-to-one $$ \begin{aligned} &f(x) = -2(x-1)^2 + 3\ &f(0) = -2(0-1)^2 + 3 = -2(1) + 3 = 1\ &f(2) = -2(2-1)^2 + 3 = -2(1) + 3 = 1\ &f(0) = f(2) = 1 \text{ with } 0 eq 2 \implies \text{Not one-to-one} \end{aligned} $$ ## Question 1 Function ## Question 2 Function ## Question 3 Incomplete (The definition of $f(x)$ is cut off in the image) ## Question 4 Incomplete (The definition of $f(x)$ is cut off in the image) ## Question 5 $f(0) = 1$ and $f(2) = 1$. Since two distinct inputs produce the same output, the function is not one-to-one. { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "One-to-One Functions" ] }

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Explanation:

Determine if the relations are functions

Evaluate the function

Show the function is not one-to-one

Answer:

Question 1

Question 2

Question 3

Question 4

Question 5