Question 1.
Consider the function

a. Graph the function
b. List the intercepts

Question 2.
Consider the function $f(x) = x^2 - 5x + 2$,
a. Determine whether function $f$ is even, odd or neither.
b. Find the average rate of change of $f$ from $x_0$ to $x_0 + h$, where $h$ is real.

Question 3.
Given the function $f(x) = (x + 2)^2 - 1$. Graph this quadratic function using the transformation.

Question 4.
Funfest Football Company has determined that the marginal cost C dollars of manufacturing x football clubs may be expressed by the quadratic function $C(x) = 5.3x^2 - 1081.2x + 56,100$
a. How many clubs should be manufactured to minimize the marginal cost?
b. At this level of production, what is the marginal cost?

Question 5.
a) Show that the following polynomial function has at least one zero in the given interval: $f(x) = 2x^4 - 3x^3 + 12x^2 - 7x - 1$ ; $[0; 1]$
b) Find any horizontal, vertical, or oblique asymptotes of the following function
$f(x) = \frac{x^3 + 4x^2 - 3x - 5}{x^2 - 3x + 2}$

Question 6.
Fourth-degree polynomial with real coefficients with zeros: $1, -2, 3 + 2i$. Find the remaining zero and write a polynomial meets the above conditions.

Question 7.
Find the inverse of each function and check your answer
a) $f(x) = \frac{5x+2}{-4x+3}$
b) $f(x) = 3 - \sqrt[3]{4x + 3}$

Question 8.
a) Write the following expression as the sum and/or difference of logarithms
$\log_5 \frac{3x^2 + 6x + 3}{\sqrt[5]{(x^2 + 1)^4}}, x > -1$
b) Given $\log_{12} 18 = a$; $\log_{24} 54 = b$. Prove that $ab + 5(a - b) = 1$

Question 9.
Solve the following equations
a) $\log_2 (3x - 1) + \log_2 (10 - 2x) = 4$
b) $(3 - 2\sqrt{2})^{x^2 - 4x} = (3 + 2\sqrt{2})^{6-x}$

Question 10.
a) If $10,000 is invested at 8% compounded monthly, how much is there after 18 months?
b) If you want to have $12,000 in 15 months, how much do you need to place in a savings account now that pays 10% compounded quarterly.