given the function (f(x) = log_{10}(2x + 10) - 4), find the following:

a) find the domain of (f). enter your answer in interval notation.

b) find the vertical asymptote(s) of (f). if there are multiple asymptotes, separate them with a comma.

Question

given the function (f(x) = log_{10}(2x + 10) - 4), find the following:

a) find the domain of (f). enter your answer in interval notation.

b) find the vertical asymptote(s) of (f). if there are multiple asymptotes, separate them with a comma.

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Logarithmic Domain", "Vertical Asymptotes" ], "current_concepts": [ "Logarithmic Domain", "Vertical Asymptotes" ] } ## Determine the domain of the function $$ \begin{aligned} 2x + 10 &> 0 \ 2x &> -10 \ x &> -5 \ \text{Domain} &= (-5, \infty) \end{aligned} $$ ## Find the vertical asymptote $$ \begin{aligned} 2x + 10 &= 0 \ 2x &= -10 \ x &= -5 \end{aligned} $$ ## Question a $(-5, \infty)$ ## Question b $x = -5$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Logarithmic Domain" ] }

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QUESTION IMAGE

Question

Explanation:

Determine the domain of the function

Find the vertical asymptote

Answer:

Question a

Question b