the graph of $f(x) = \log x + 3$ is the graph of $g(x) = \log x$ translated 3 units up.

if you are given the graph of $g$, how could you graph $f(x) = \log x + 3$?
for each point on the graph of $g$,

Question

the graph of $f(x) = \log x + 3$ is the graph of $g(x) = \log x$ translated 3 units up.

if you are given the graph of $g$, how could you graph $f(x) = \log x + 3$?
for each point on the graph of $g$,

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": [ "Logarithmic Function Transformations", "Vertical Translation" ], "new_concepts": [], "current_concepts": [ "Logarithmic Function Transformations", "Vertical Translation" ] } ## Analyze the function transformation Using the *Logarithmic Function Transformations* and *Vertical Translation* knowledge points $$ \begin{aligned} &f(x) = g(x) + 3\ &f(x) = \log x + 3 \end{aligned} $$ ## Determine the effect on coordinates Using the *Vertical Translation* knowledge point $$ \begin{aligned} &(x, y) \to (x, y + 3) \end{aligned} $$ If you are given the graph of g, how could you graph $f(x) = \log x + 3$? For each point on the graph of g, add 3 to the y-coordinate { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Logarithmic Function Transformations" ] }

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Question

Explanation:

Analyze the function transformation

Determine the effect on coordinates

Answer: