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1)\(Compute \lfloor \log_3 1000 \rfloor.\)

 

2)Among the following functions, let a be the number of functions that are monotonically increasing, let b be the number of functions that are monotonically decreasing, and let c be the number of functions that are neither monotonically increasing nor monotonically decreasing. Enter your answer in the form "a,b,c".

 

\(\begin{align*} y &= x^4 \\ y &= \log_{\frac{1}{2}} x \\ y &= x^2 - 2x \\ y &= \frac{1}{x^2} \\ y &= -\frac{1}{\sqrt{x}} \\ y &= \sqrt[3]{x + 4} \\ y &= 11^{-x} \\ y &= 5 - 3x \end{align*}\)

3)Among the following functions, let a be the number of functions that are even, let b be the number of functions that are odd, and let c be the number of functions that are neither even nor odd. Enter your answer in the form "a,b,c".

\(\begin{align*} y &= \frac{x}{x^2 - 1} \\ y &= \frac{x}{x - 1} \\ y &= 2x - 11 \\ y &= \log_3 (x^2 - 1) \\ y &= 2^{-x} \\ y &= 6x^5 + x + \frac{2}{x^3} \\ y &= \sqrt[3]{x} \\ y &= \lfloor x \rfloor \end{align*}\)

 May 12, 2019
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1. The answer is 18.

 

2. The answer is (3,1,4).

 

3. The answer is (6,0,2).

 Nov 3, 2019

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