Unit 6 Flexible Practice

Domain of $\frac{1}{x+5}$.

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Can rational function have all-real domain?

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Correct this reasoning and identify the first unsafe assumption: A frequent error is simplifying before recording the original exclusions.

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Hole of $\frac{x^2-1}{x-1}$.

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What sets hole y-value?

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Connect two representations for this example: Analyze $\frac{x^2-9}{x-3}$. Describe what a graph, table, mapping, or algebraic form would have to show.

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VA of $\frac{3}{x-5}$.

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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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Connect two representations for this example: Analyze $\frac{1}{x-2}$ near $2$. Describe what a graph, table, mapping, or algebraic form would have to show.

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HA of $\frac{1}{x+2}$.

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Explain why this conclusion is valid: Horizontal asymptote $y=\frac{5}{2}$. Use the foundation problem as evidence: Analyze $\frac{5x^3-2}{2x^3+x}$.

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Connect two representations for this example: Analyze $\frac{5x^3-2}{2x^3+x}$. Describe what a graph, table, mapping, or algebraic form would have to show.

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Polynomial asymptote of $\frac{x^3+1}{x}$.

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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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Create a nearby example by changing one number or condition in this prompt: When slant occurs. Predict the effect, solve your new example, and compare it with the original.

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Y-intercept.

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Solve the representation example, then name the feature of intercepts and sign charts that it illustrates: Y-intercept.

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Create a nearby example by changing one number or condition in this prompt: Critical values of $\frac{x}{(x-2)(x+4)}$. Predict the effect, solve your new example, and compare it with the original.

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Can HA be crossed?

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Solve the representation example, then name the feature of complete rational graph construction that it illustrates: Can HA be crossed?

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Create a nearby example by changing one number or condition in this prompt: Can VA be crossed? Predict the effect, solve your new example, and compare it with the original.

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X-intercept of $\frac{x-2}{x+3}$.

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Solve the representation example, then name the feature of rational equations and function intersections that it illustrates: Solve$$\frac{2}{x}=\frac{1}{x-3}$$

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Write a short verification checklist for rational equations and function intersections, then apply it to one worked example from this lesson.

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Which endpoints may be included?

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Solve the representation example, then name the feature of rational inequalities that it illustrates: Solve$$\frac{1}{x}<0$$

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Write a short verification checklist for rational inequalities, then apply it to one worked example from this lesson.

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If $x$ doubles in $\frac{k}{x}$.

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Correct this reasoning and identify the first unsafe assumption: A frequent error is placing a factor in the numerator or denominator contrary to the wording.

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Write a short verification checklist for variation and rational models, then apply it to one worked example from this lesson.

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Can decomposition restore exclusions?

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Correct this reasoning and identify the first unsafe assumption: A frequent error is omitting a repeated-power term.

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