Nonlinear Functions Practice

Sample questions

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1. Sample 1difficulty 2/5

   A bacteria culture doubles every 4 hours. If 200 bacteria are present at noon, how many will be present at 8 PM that day?

   • A

     400

   • B

     800

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   • C

     600

   • D

     1600

   Why

   8 PM is 8 hours later = 2 doubling periods. $200 \cdot 2^2 = 800$.

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2. Sample 2difficulty 2/5

   If $f(x) = 2x + 1$ and $g(x) = x^2$, what is $f(g(3))$?

   • A

     $13$

   • B

     $19$

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   • C

     $49$

   • D

     $10$

   Why

   $g(3) = 9$, then $f(9) = 2(9) + 1 = 19$.

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3. Sample 3difficulty 2/5

   The graph of $y = f(x)$ is shifted 4 units up. Which equation represents the new graph?

   • A

     $y = f(x) + 4$

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   • B

     $y = f(x - 4)$

   • C

     $y = f(x) - 4$

   • D

     $y = f(x + 4)$

   Why

   A vertical shift up by $k$ units adds $k$ to the function: $y = f(x) + 4$.

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4. Sample 4difficulty 2/5

   Which expression is equivalent to $x^{1/3}$?

   • A

     $\dfrac{1}{x^3}$

   • B

     $\sqrt[3]{x}$

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   • C

     $3x$

   • D

     $\sqrt{x}$

   Why

   Fractional exponent $1/n$ corresponds to the $n$th root: $x^{1/3} = \sqrt[3]{x}$.

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5. Sample 5difficulty 2/5

   What is the value of $7^0$?

   • A

     undefined

   • B

     $0$

   • C

     $1$

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   • D

     $7$

   Why

   Any nonzero base raised to the 0 power equals $1$.

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