activity - graphing cube root functions

find the required values and graph the function (y = 3\sqrt3{x - 2} + 1).

value: 4

match the items.
a. 3
b. 2
c. (2, 1)
d. 1

1. (a)
2. (h)
3. (k)
4. vertex

so, the graph of the given function is as follows:

Question

activity - graphing cube root functions

find the required values and graph the function (y = 3\sqrt3{x - 2} + 1).

value: 4

match the items.
a. 3
b. 2
c. (2, 1)
d. 1

1. (a)
2. (h)
3. (k)
4. vertex

so, the graph of the given function is as follows:

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Cube Root Function", "Function Transformations" ], "new_concepts": [ "Vertex of Cube Root Function" ], "current_concepts": [ "Cube Root Function", "Function Transformations", "Vertex of Cube Root Function" ] } ## Identify parameters of the function Using the *Cube Root Function* and *Function Transformations* knowledge points $$ \begin{aligned} &y = a\sqrt[3]{x - h} + k \ &y = 3\sqrt[3]{x - 2} + 1 \ &a = 3, \quad h = 2, \quad k = 1 \end{aligned} $$ ## Determine the vertex Using the *Cube Root Function* and *Function Transformations* knowledge points $$ \begin{aligned} &\text{Vertex} = (h, k) \ &\text{Vertex} = (2, 1) \end{aligned} $$ ## Match the items Using the *Cube Root Function* and *Function Transformations* knowledge points $$ \begin{aligned} &1. \ a ightarrow \text{a. } 3 \ &2. \ h ightarrow \text{b. } 2 \ &3. \ k ightarrow \text{d. } 1 \ &4. \ \text{Vertex} ightarrow \text{c. } (2, 1) \end{aligned} $$ 1. a 2. b 3. d 4. c { "elements": [ { "type": "functiongraph", "params": [ { "js": "3 * Math.cbrt(x - 2) + 1", "latex": "3\sqrt[3]{x - 2} + 1" }, -8, 10 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3, "name": "y = 3\sqrt[3]{x-2}+1", "withLabel": true } }, { "type": "point", "params": [ [2, 1] ], "properties": { "name": "Vertex (2, 1)", "size": 5, "strokeColor": "#F2557F", "fillColor": "#F2557F", "withLabel": true } } ], "timestamps": [0.5, 1.0] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Cube Root Function" ] }

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QUESTION IMAGE

Question

Explanation:

Identify parameters of the function

Determine the vertex

Match the items

Answer: