Unit 2 Flexible Practice

Write cost for $\$9$ plus $\$2$ per movie.

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Horizontal axis for cost as function of hours.

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Correct this reasoning and identify the first unsafe assumption: A frequent error is manipulating symbols before defining what they measure.

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Write a short verification checklist for quantities, variables, and dependency, then apply it to one worked example from this lesson.

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Give a function not one-to-one.

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Solve the representation example, then name the feature of relations and functions that it illustrates: Is $y=x^2$ a function of $x$?

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Create a nearby example by changing one number or condition in this prompt: Give a function not one-to-one. Predict the effect, solve your new example, and compare it with the original.

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For $g(x)=x^2+1,$ find $g(-3)$.

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Solve the representation example, then name the feature of function notation, evaluation, and solving that it illustrates: For $g(x)=x^2+1,$ find $g(-3)$.

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Create a nearby example by changing one number or condition in this prompt: For $f(x)=x^2,$ solve $f(x)=16$. Predict the effect, solve your new example, and compare it with the original.

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Cost $\$25$ plus $\$8$ per person.

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Explain why this conclusion is valid: A linear candidate is $f(x)=3x+5$. Use the foundation problem as evidence: Values $5,8,11,14$ occur at $x=0,1,2,3$.

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Connect two representations for this example: Values $5,8,11,14$ occur at $x=0,1,2,3$. Describe what a graph, table, mapping, or algebraic form would have to show.

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Domain of $\frac{1}{x+4}$.

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Domain of $sqrt(x^2-9)$.

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Correct this reasoning and identify the first unsafe assumption: A frequent error is checking only one restriction or using the simplified formula's larger domain.

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Physical domain of side length $s$.

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Define interpolation.

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Correct this reasoning and identify the first unsafe assumption: A frequent error is reporting all real numbers for a model involving time, length, population, or counts.

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

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Point for $f(2)=0$.

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Solve the representation example, then name the feature of range and global graph behavior that it illustrates: Maximum y-intercepts for a function.

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Create a nearby example by changing one number or condition in this prompt: Point for $f(2)=0$. Predict the effect, solve your new example, and compare it with the original.

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Meaning of overlapping intervals.

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Solve the representation example, then name the feature of piecewise-defined functions that it illustrates: Meaning of overlapping intervals.

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Create a nearby example by changing one number or condition in this prompt: Meaning of omitted boundary. Predict the effect, solve your new example, and compare it with the original.

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Average rate of $x^2-3x$ from $2$ to $5$.

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Explain why this conclusion is valid: $5$. Use the foundation problem as evidence: Find average rate of $x^2$ from $1$ to $4$.

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Connect two representations for this example: Find average rate of $x^2$ from $1$ to $4$. Describe what a graph, table, mapping, or algebraic form would have to show.

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Define residual.

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Give extrapolation example.

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Correct this reasoning and identify the first unsafe assumption: A frequent error is choosing the smoothest graph or highest fit statistic without checking meaning.

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