Quantities, Variables, and Mathematical Objects: mastery answer key

In f_a(x) $= ax^{2},$ explain the role of $a$.

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A graph labels a point P. Must P be a number?

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Create a quantity dictionary for $p = 3s + 2$ where $s$ is side length in cm and $p$ is perimeter in cm.

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Which values are reasonable for the number $n$ of students in a room?

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Which values are reasonable for elapsed time $t$ in a race model?

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In V $=$ lwh, which quantity depends on the other three?

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A student calls $^\circ\mathrm{C}$ a variable in T $= 20^\circ\mathrm{C}$. Repair the claim.

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Give one context where $k$ is a constant and one where it is a parameter.

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For $y = 2x +$ b, what stays fixed while viewing one line?

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Explain why using $m$ for both mass and meters in one formula is ambiguous.

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A tank starts with $100$ L and drains at $\frac{r L}{min}$. Name roles in V $= 100 -$ rt.

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Write a complete variable declaration for the cost of $x$ adult tickets at $\$14$ each.

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In V $= 12 + 4t,$ V is water volume in liters and $t$ is time in minutes. Identify the input, output, initial value, rate, units, and contextual domain.

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A student says $x$ is always independent because it is usually on the horizontal axis. Give a counterexample.

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Create a four-row table for C $= 3 + 2m$ using $m = 0, 1, 2.5, 4,$ then describe what stays constant.

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A theater model R $= 18n$ gives revenue R from $n$ tickets. Explain why $n = 2.5$ may be algebraically evaluable but contextually invalid.

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Classify $5a^{2} - 3a + 1$.

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Classify $2n + 4 = 18$.

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