Unit 3 Flexible Practice

$\frac{Domain}{range}$ of $x^2$.

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Exponential table pattern.

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Correct this reasoning and identify the first unsafe assumption: A frequent error is naming a family from appearance without checking restrictions.

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Write a short verification checklist for parent-function atlas, then apply it to one worked example from this lesson.

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Map under -f(x).

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Solve the representation example, then name the feature of coordinate mappings and transformation logic that it illustrates: Map under$$f(x-2)$$

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Create a nearby example by changing one number or condition in this prompt: Map under -f(x). Predict the effect, solve your new example, and compare it with the original.

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Range of $sqrt(x)-2$.

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Solve the representation example, then name the feature of vertical translations that it illustrates: Range of$$sqrt(x)-2$$

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Create a nearby example by changing one number or condition in this prompt: HA of $5^x+7$. Predict the effect, solve your new example, and compare it with the original.

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Vertex of $(x-7)^2$.

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Explain why this conclusion is valid: Endpoint $(4,0),$ domain $[4,∞)$. Use the foundation problem as evidence: Describe $sqrt(x-4)$.

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Connect two representations for this example: Describe $sqrt(x-4)$. Describe what a graph, table, mapping, or algebraic form would have to show.

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Reflect $x^2$ across x-axis.

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Classify $x^2+x$.

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Correct this reasoning and identify the first unsafe assumption: A frequent error is confusing -f(x) with $f(-x)$.

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Describe $5|x|$.

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Range $[1,4]$ under $-2f$.

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Correct this reasoning and identify the first unsafe assumption: A frequent error is multiplying horizontal coordinates by $c$ instead of dividing.

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Write a short verification checklist for vertical and horizontal scaling, then apply it to one worked example from this lesson.

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Asymptotes of $\frac{2}{x+1}-3$.

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Solve the representation example, then name the feature of combined transformations that it illustrates: Endpoint of$$-sqrt(x-5)+4$$

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Create a nearby example by changing one number or condition in this prompt: Asymptotes of $\frac{2}{x+1}-3$. Predict the effect, solve your new example, and compare it with the original.

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If $f(2)=5,g(2)=-1$.

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Solve the representation example, then name the feature of sums and differences of functions that it illustrates: If$$f(2)=5,g(2)=-1$$

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Create a nearby example by changing one number or condition in this prompt: Domain $sqrt(x-3)+ln x$. Predict the effect, solve your new example, and compare it with the original.

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Domain $\frac{x+1}{x}^2$.

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Explain why this conclusion is valid: $\frac{f}{g}=x+1$ for $x\ne 1,$ with a hole at $(1,2)$. Use the foundation problem as evidence: $f=x^2-1,g=x-1$.

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Connect two representations for this example: $f=x^2-1,g=x-1$. Describe what a graph, table, mapping, or algebraic form would have to show.

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Vertex $(1,2),$ point $(3,10)$.

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One clue for uniqueness.

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Correct this reasoning and identify the first unsafe assumption: A frequent error is guessing from appearance and never checking a second point or domain.

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