Problem

For \(y~=~-\sqrt[3]{x}~+~5\), describe the parent-graph effect, state the limits as \(x\) approaches \(\text{positive}~\text{and}~\text{negative}~\text{infinity}\), and explain both end directions.

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Parent effect: no reflection of ∛x. Right end: x→∞ gives y→∞. Left end: x→−∞ gives y→−∞. Evidence: the leading negative is ignored.

Parent effect: x-axis reflection of ∛x. Right end: x→∞ gives y→−∞. Left end: x→−∞ gives y→∞. Evidence: reflection reverses both end directions.

Parent effect: x-axis reflection of ∛x. Right end: x→∞ gives y→∞. Left end: x→−∞ gives y→−∞. Evidence: the reflection direction is ignored.

Parent effect: x-axis reflection of ∛x. Right end: x→∞ gives y→−∞. Left end: not reported. Evidence: only one end of an all-real-domain function is analyzed.

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For \(y~=~-\sqrt[3]{x}~+~5\), describe the parent-graph effect, state the limits as \(x\) approaches \(\text{positive}~\text{and}~\text{negative}~\text{infinity}\), and explain both end directions.

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