below is the graph of $y=b^x$. find $b$.

$b = $

Question

below is the graph of $y=b^x$. find $b$.

$b = $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Exponential Function Graphs" ], "new_concepts": [], "current_concepts": [ "Exponential Function Graphs", "Exponential Evaluation" ] } ## Identify a clear point on the graph Using the *Exponential Function Graphs* knowledge point $$ \begin{aligned} &\text{The graph passes through the point } (-1, 3).\ &\text{At } x = 0, \text{ the graph passes through } (0, 1). \end{aligned} $$ ## Substitute the point into the equation Using the *Exponential Function Graphs* knowledge point $$ \begin{aligned} &y = b^x\ &3 = b^{-1} \end{aligned} $$ ## Solve for b Using the *Exponential Function Graphs* knowledge point $$ \begin{aligned} &3 = \frac{1}{b}\ &b = \frac{1}{3} \end{aligned} $$ Below is the graph of $y=b^x$. Find $b$. $b =$ $\frac{1}{3}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Function Graphs" ] }

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Question

Explanation:

Identify a clear point on the graph

Substitute the point into the equation

Solve for b

Answer: