Problem

A logarithmic graph has vertical asymptote \(x~=~-3\) and point \((-2,~0)\) on its right-hand branch. State every graph feature and parameter determined by this information, then state what remains undetermined.

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Determined: logarithmic family, asymptote x = −3, domain x > −3, range all real numbers, anchor and x-intercept (−2, 0), and argument shift x + 3. Undetermined: base, vertical scale or reflection, and further exact anchors.

Determined: logarithmic family and range all real numbers. Undetermined: the asymptote, domain, argument shift, intercept, base, scale or reflection, and all anchors, because neither supplied feature fixes any graph property.

Determined: logarithmic family, asymptote x = −3, domain x > −3, range all real numbers, base 10, no reflection, anchor (−2, 0), and further anchor (7, 1). Undetermined: none of these features.

Determined: logarithmic family, asymptote x = −3, domain x < −3, range all real numbers, and a left-hand branch. Undetermined: whether (−2, 0) is an intercept, the argument shift, base, scale, and further anchors.

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A logarithmic graph has vertical asymptote \(x~=~-3\) and point \((-2,~0)\) on its right-hand branch. State every graph feature and parameter determined by this information, then state what remains undetermined.

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