solve $\log (x + 1) = -x^2 + 10$ by graphing.

which equations should be graphed?

$y_1 = -x^2$
$y_1 = -x^2 + 10$
$y_2 = \frac{\log x}{\log 1}$
$y_2 = \log (x + 1)$

Question

solve $\log (x + 1) = -x^2 + 10$ by graphing.

which equations should be graphed?

$y_1 = -x^2$
  $y_1 = -x^2 + 10$
  $y_2 = \frac{\log x}{\log 1}$
  $y_2 = \log (x + 1)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Solving Exponential Equations Graphically" ], "new_concepts": [ "Graphical Solution of Equations" ], "current_concepts": [ "Solving Exponential Equations Graphically", "Graphical Solution of Equations" ] } ## Identify the system of equations Using the *Solving Exponential Equations Graphically* knowledge point $$ \begin{aligned} &\text{Given equation: } \log(x + 1) = -x^2 + 10\ &y_1 = -x^2 + 10\ &y_2 = \log(x + 1) \end{aligned} $$ ## Match with the given options Using the *Solving Exponential Equations Graphically* knowledge point $$ \begin{aligned} &\text{Option 1: } y_1 = -x^2 \quad (\text{Incorrect})\ &\text{Option 2: } y_1 = -x^2 + 10 \quad (\text{Correct})\ &\text{Option 3: } y_2 = \frac{\log x}{\log 1} \quad (\text{Incorrect})\ &\text{Option 4: } y_2 = \log(x + 1) \quad (\text{Correct}) \end{aligned} $$

$$y_1 = -x^2$$

$$y_1 = -x^2 + 10$$

$$y_2 = \frac{\log x}{\log 1}$$

$$y_2 = \log(x + 1)$$

{ "elements": [ { "type": "functiongraph", "params": [ { "js": "-x*x + 10", "latex": "y = -x^2 + 10" }, -4, 4 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2, "name": "y_1 = -x^2 + 10", "withLabel": true } }, { "type": "functiongraph", "params": [ { "js": "Math.log10(x + 1)", "latex": "y = \log(x + 1)" }, -0.99, 8 ], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2, "name": "y_2 = \log(x + 1)", "withLabel": true } } ], "timestamps": [0.5, 1.0] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Graphical Solution of Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the system of equations

Match with the given options

Answer: