Unit 6 Investigation

Explain why this conclusion is valid: $x\ne 3,-2$. Use the foundation problem as evidence: Domain of $\frac{x}{x^2-x-6}$.

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Explain why this conclusion is valid: Left -∞, right $+∞$. Use the foundation problem as evidence: Analyze $\frac{1}{x-2}$ near $2$.

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Explain why this conclusion is valid: $x+1+\frac{2}{x-1},$ so asymptote $y=x+1$. Use the foundation problem as evidence: Analyze $\frac{x^2+1}{x-1}$.

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Correct this reasoning and identify the first unsafe assumption: A frequent error is omitting a hole or connecting branches across a vertical asymptote.

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Connect two representations for this example: Solve $\frac{x+3}{x-4}\le 0$. Describe what a graph, table, mapping, or algebraic form would have to show.

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