which function is shown in the graph?
$f(x) = \log_{0.2} x$
$f(x) = \log_{2} x$
$f(x) = \log_{5} x$
$f(x) = \log_{10} x$

what is the domain of the function?
what is the range of the function?

Question

which function is shown in the graph?
$f(x) = \log_{0.2} x$
$f(x) = \log_{2} x$
$f(x) = \log_{5} x$
$f(x) = \log_{10} x$

what is the domain of the function?
what is the range of the function?

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Logarithmic Functions", "Domain of Exponential Functions", "Range of Exponential Functions" ], "new_concepts": [ "Domain of Logarithmic Functions", "Range of Logarithmic Functions" ], "current_concepts": [ "Logarithmic Functions", "Domain of Logarithmic Functions", "Range of Logarithmic Functions" ] } ## Identify the logarithmic function from the graph Using the *Logarithmic Functions* knowledge point $$ \begin{aligned} &\text{Points on the graph: } (1, 0), (5, 1), (0.2, -1)\ &f(x) = \log_b x \implies 1 = \log_b 5 \implies b^1 = 5 \implies b = 5\ &f(x) = \log_5 x \end{aligned} $$ ## Determine the domain of the function Using the *Logarithmic Functions* knowledge point $$ \begin{aligned} &\text{The function } f(x) = \log_5 x \text{ is defined only for positive real numbers.}\ &\text{Domain: } (0, \infty) \text{ or } \{x \mid x > 0\} \end{aligned} $$ ## Determine the range of the function Using the *Logarithmic Functions* knowledge point $$ \begin{aligned} &\text{The output of a logarithmic function can be any real number.}\ &\text{Range: } (-\infty, \infty) \text{ or all real numbers} \end{aligned} $$ ## Question 1 (A) $f(x) = \log_{0.2} x$

(B) $f(x) = \log_2 x$

(C) $f(x) = \log_5 x$

(D) $f(x) = \log_{10} x$ ## Question 2 The domain of the function is $(0, \infty)$ (or $x > 0$). ## Question 3 The range of the function is $(-\infty, \infty)$ (or all real numbers). { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Logarithmic Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the logarithmic function from the graph

Determine the domain of the function

Determine the range of the function

Answer:

Question 1

Question 2

Question 3