Problem Set 0

Submission

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Problems

1. Determine which sets of numbers do the following numbers belong to amon Naturals $ \mathbb{N} $, Integers $ \mathbb{Z} $, Rationals $ \mathbb{Q} $ , and Reals $ \mathbb{R} $. Select all that apply.

   a. 25

   b. 32.5

   c. 1/3

   d. π/3

2. Determine which kind of function is represented by the following expression on $x$.

   a. 35

   b. $2x$

   c. $2x +5$

   d. $x^{2} + 3x -1$

   e. $2^{x}$

   f. $\log(x) - \log(2x)$

3. Solve the following systems of equations.

   a. $x-y = -1$ and $3x = 3(y+2)$

   b. $x-y = -1$ and $3x = y+3$

4. Factor the following polynomials

   a. $9 + 12x + 4x^{2}$

   b. $25 + 20x + 4 x^{2}$

   c. $25 - 20x + 4 x^{2}$

   d. $9x^2 - 243$

5. Compute the following values.

   a. $\log_{10}(10000)$

   b. $\log_{2}(8) - \log_{2}(32)$

   c. $\log_{2}(1/16)$

6. Find the values of x that satisfy the equations below.

   a. $\log_{2}(x) + \log_4(x) = 3$

   b. $4^{x} - 2^{x+1} = 0$

   c. $10^{2x+2} = 50^{x+1}$