1. If f(x) = x^2 - 3x determine the following
(i) f(-2) (ii) f(-2a) (iii) f(2-a)
2. (i) Use your calculator to sketch a graph of the function f(x) = 2/sqrt(9 - x^2)
(ii) Explain the restrictions to the domain of the function.
(iii) Name and describe the feature of the graph that occurs at x = -3 and x=3
3. (i) Find the points where the straight line -3x + 4y - 18 = 0 crosses each axis.
(ii) Sketch the graph of the linear function y = f(x) represented by this equation.
(iii) What is the slope of this line?
(iv) The line x + y - 1 = 0 crosses the line -3x + 4y - 18 = 0 at the point (-2, 3). Verify that this statement is true.
4. A produce wholesaler sells 1kg bags of mixed nuts (peanuts & cashews) for $5.85. If peanuts sell at $4.50/kg and cashews at $9.00/kg, what quantity of each type of nut must be in each bag to make them economic?
5. (i) Determine the roots of the function f(x) = 2 x^2 - 7x + 3
(ii) Determine the extreme value of this function f(x)
(iii) Sketch the graph of this function, clearly showing the points determined in parts (i) and (ii)
(iv) Sketch the function f(x) = 2(x+1)^2 - 7(x+1) +3 on the same set of axes and explain how it relates to the function in (iii)
6. (a) Show that log_t p+3(log_t 2 - log_t q) may be written as log_t 8p/q^3
(b) The demand function for a product is p = 100/In(q+1), where p is the price of the item in dollars and q is the demand in thousands of items.
(i) Find the price if 1100 items are demanded.
(ii) By first solving the above equation for q, determine what level of demand would set the price at $20
This solution is comprised of detailed explanation and step-by-step calculation of the given problems and provides students with a clear perspective of the underlying concepts.