type the correct answer in the box. use numerals instead of words.

the graphs of functions $f$ and $g$ are shown.

function $g$ is defined as $g(x) = f(x) - c$. what is the value of $c$?

Question

type the correct answer in the box. use numerals instead of words.

the graphs of functions $f$ and $g$ are shown.

function $g$ is defined as $g(x) = f(x) - c$. what is the value of $c$?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Logarithmic Functions" ], "new_concepts": [ "Vertical Translation" ], "current_concepts": [ "Logarithmic Functions", "Vertical Translation" ] } ## Identify key points on the graphs of $f$ and $g$ $$ \begin{aligned} &f(1) = 0 \ &g(1) = -3 \end{aligned} $$ ## Set up the translation equation $$ \begin{aligned} &g(x) = f(x) - c \ &g(1) = f(1) - c \end{aligned} $$ ## Solve for $c$ $$ \begin{aligned} &-3 = 0 - c \ &c = 3 \end{aligned} $$ Function $g$ is defined as $g(x) = f(x) - c$. What is the value of $c$? 3 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Vertical Translation" ] }

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QUESTION IMAGE

Question

Explanation:

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

Set up the translation equation

Solve for \(c\)

Answer: