the graphs of functions $f$ and $g$ are shown.
function $g$ is defined as $g(x) = kf(x)$. what is the value of $k$?
the value of $k$ is .

Question

the graphs of functions $f$ and $g$ are shown.
function $g$ is defined as $g(x) = kf(x)$. what is the value of $k$?
the value of $k$ is  .

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Function Transformations" ], "new_concepts": [], "current_concepts": [ "Function Transformations", "Square Root Functions" ] } ## Identify corresponding points on the graphs of $f$ and $g$ $$ \begin{aligned} &\text{At } x = 4: \quad f(4) = 2, \quad g(4) = 4 \ &\text{At } x = 9: \quad f(9) = 3, \quad g(9) = 6 \ &\text{At } x = 16: \quad f(16) = 4, \quad g(16) = 8 \end{aligned} $$ ## Set up the transformation equation to solve for $k$ $$ \begin{aligned} &g(x) = k \cdot f(x) \ &g(4) = k \cdot f(4) \ &4 = k \cdot 2 \ &k = 2 \end{aligned} $$ ## Verify the value of $k$ with another point $$ \begin{aligned} &g(9) = 2 \cdot f(9) \ &6 = 2 \cdot 3 = 6 \end{aligned} $$ Function $g$ is defined as $g(x) = k f(x)$. What is the value of $k$? The value of $k$ is 2. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Function Transformations" ] }

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Question

Explanation:

Identify corresponding points on the graphs of \(f\) and \(g\)

Set up the transformation equation to solve for \(k\)

Verify the value of \(k\) with another point

Answer: