graph the function.

\f(x)=\sqrt{x}+5\

plot four points on the graph of the function: the leftmost point and three additional points. then click on the graph-a-function button.

Question

graph the function.

\f(x)=\sqrt{x}+5\

plot four points on the graph of the function: the leftmost point and three additional points. then click on the graph-a-function button.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [], "new_concepts": [ "Square Root Function Graphing", "Domain of Radical Functions" ], "current_concepts": [ "Square Root Function Graphing", "Domain of Radical Functions", "Function Transformations" ] } ## Determine the domain and leftmost point $$ \begin{aligned} x + 5 &\ge 0 \implies x \ge -5 \ f(-5) &= \sqrt{-5 + 5} = 0 \ \text{Leftmost point: } &(-5, 0) \end{aligned} $$ ## Calculate three additional integer points $$ \begin{aligned} x = -4 &\implies f(-4) = \sqrt{-4 + 5} = 1 \implies (-4, 1) \ x = -1 &\implies f(-1) = \sqrt{-1 + 5} = 2 \implies (-1, 2) \ x = 4 &\implies f(4) = \sqrt{4 + 5} = 3 \implies (4, 3) \end{aligned} $$ The four points to plot on the graph of $f(x) = \sqrt{x+5}$ are: - Leftmost point: $(-5, 0)$ - Additional point 1: $(-4, 1)$ - Additional point 2: $(-1, 2)$ - Additional point 3: $(4, 3)$ { "elements": [ { "type": "point", "params": [[-5, 0]], "properties": { "name": "(-5,0)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[-4, 1]], "properties": { "name": "(-4,1)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[-1, 2]], "properties": { "name": "(-1,2)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[4, 3]], "properties": { "name": "(4,3)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "functiongraph", "params": [ { "js": "Math.sqrt(x + 5)", "latex": "\sqrt{x+5}" }, -5, 13 ], "properties": { "strokeColor": "#5583F2", "strokeWidth": 3 } } ], "timestamps": [0.2, 0.4, 0.6, 0.8, 1.2] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Square Root Function Graphing" ] }

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Question

Explanation:

Determine the domain and leftmost point

Calculate three additional integer points

Answer: