1. Express the number in terms of i.
√(-18)
-√(-9)
2. Simplify. Write answers in the form a + bi, where a and b are real numbers.
( 13 + 8i ) + ( -3 + 8i )
( 14 + 7i ) - ( 5 + 3i )
( 5 - 8i ) ( -1 + i )
3i ( 3 + 5i )
(6+5i)/(3-4i)
3. Simplify. Show work.
i^19
i^24
[(-i)^8
4. Find all real roots. Check your answers.
f (x) = -6x2 - 24x + 18
f(x) = x^(4 )-4x^3+3x2
5. Find all real or complex solutions.
t^4 = 16
6. For each function:
Find the vertex; b) Find the axis of symmetry; c) determine whether there is a maximum or minimum value, and find that value; d) graph the function.
f(x) = x2 + 2x + 6
g(x) = x2 + 7x - 8
7. Find the zeros of the polynomial function and state the multiplicity of each.
a. f(x) = (x + 5 )3 ( x - 4 ) ( x + 1 )2
b. (x2 - 4 )2 = f(x)
c. f(x) = x3 - x2 - 2x + 2
8. Determine the domain of the function
f(x) = (4x-9)/(4x+40)
9. Determine the horizontal asymptote of the graph of the function. Sketch the graph.
f(x) = (2x^2+5)/(3x^2 - 4)
10. Determine the vertical asymptote of the graph of the function. Sketch the graph.
f(x) = (x - 7)/(3 - x)
11. Find all real solutions. Check your answers.
x/(10x+4) = 6
12. After working for a company for 15 months, an employee has earned 20 vacation days. At this rate, how much longer will the employee have to work in order to get a 6-week vacation (30 work days)?
13. Theorem 6.2- Suppose f(x) = logb (x).
• The domain of f is (0, ∞) and the range of f is (-∞, ∞).
• (1, 0) is on the graph of f and x = 0 is a vertical asymptote of the graph of f.
• f is one-to-one, continuous and smooth
• b a = c if and only if logb (c) = a. That is, logb (c) is the exponent you put on b to obtain c.
• logb (b x ) = x for all x and b logb (x) = x for all x > 0
• If b > 1: - f is always increasing - As x → 0 +, f(x) → -∞ - As x → ∞, f(x) → ∞ - The graph of f resembles: y = logb (x), b > 1
• If 0 < b < 1: - f is always decreasing - As x → 0 +, f(x) → ∞ - As x → ∞, f(x) → -∞ - The graph of f resembles: y = logb (x), 0 < b < 1
For this problem, use this part, b a = c if and only if logb (c) = a from Theorem 6.2 to rewrite the given equation in the other form. That is, rewrite the exponential equations as logarithmic equations and rewrite the logarithmic equations as exponential equations.of the above listed Theorem to answer the problem
log(0.1) = -1