pretest: functions

$h(x) = \sqrt{x}$ $\longrightarrow$

$j(x) = -\sqrt{x-1}$ $\longrightarrow$

graph a
graph b
graph c

Question

pretest: functions

$h(x) = \sqrt{x}$ $\longrightarrow$

$j(x) = -\sqrt{x-1}$ $\longrightarrow$

graph a
graph b
graph c

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Square Root Functions", "Function Transformations" ], "new_concepts": [], "current_concepts": [ "Square Root Functions", "Function Transformations" ] } ## Analyze the parent function $h(x) = \sqrt{x}$ $$ \begin{aligned} &\text{Domain: } x \ge 0\ &\text{Key points: } (0,0), (1,1), (4,2)\ &\text{Graph: Starts at origin, curves upwards in Quadrant I (Graph A)} \end{aligned} $$ ## Analyze the transformed function $j(x) = -\sqrt{x-1}$ $$ \begin{aligned} &\text{Horizontal shift: } 1 \text{ unit right (domain: } x \ge 1\text{)}\ &\text{Vertical reflection: Reflected across the } x\text{-axis (curves downwards)}\ &\text{Key points: } (1,0), (2,-1), (5,-2)\ &\text{Graph: Starts at } (1,0) \text{ and curves downwards (not shown in the positive-only options, but matches the transformation rules)} \end{aligned} $$ ## Question 1 (A) Graph A

(B) Graph B

(C) Graph C ## Question 2 (A) Graph A

(B) Graph B

(C) Graph C

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Function Transformations" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the parent function \(h(x) = \sqrt{x}\)

Analyze the transformed function \(j(x) = -\sqrt{x-1}\)

Answer:

Question 1

Question 2