select the correct answer from each drop-down menu.

what are the key features of function $f$?

\f(x) = \log x\

function $f$ crosses the x-axis at choose an answer. as $x$ increases, the function choose an answer. as $x$ approaches its vertical asymptote of choose an answer, the function choose an answer.

Question

select the correct answer from each drop-down menu.

what are the key features of function $f$?

\f(x) = \log x\

function $f$ crosses the x-axis at choose an answer. as $x$ increases, the function choose an answer. as $x$ approaches its vertical asymptote of choose an answer, the function choose an answer.

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", "Increasing Functions" ], "new_concepts": [ "Asymptotic Behavior", "Function Intercepts" ], "current_concepts": [ "Logarithmic Functions", "Increasing Functions", "Function Intercepts", "Asymptotic Behavior" ] } ## Find the x-intercept $$ \begin{aligned} f(x) &= 0 \ \log x &= 0 \ x &= 10^0 = 1 \end{aligned} $$ ## Determine the growth behavior $$ \begin{aligned} &\text{Base of } \log x \text{ is } 10 > 1 \ &\frac{d}{dx}(\log x) = \frac{1}{x \ln 10} > 0 \quad \text{for } x > 0 \end{aligned} $$ ## Determine the vertical asymptote and limit behavior $$ \begin{aligned} &\text{Vertical asymptote: } x = 0 \ &\lim_{x \to 0^+} \log x = -\infty \end{aligned} $$ What are the key features of function $f$? $f(x) = \log x$ Function $f$ crosses the x-axis at $(1, 0)$. As x increases, the function increases. As x approaches its vertical asymptote of $x = 0$, the function decreases without bound. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Logarithmic Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Find the x-intercept

Determine the growth behavior

Determine the vertical asymptote and limit behavior

Answer: