For the functions in questions 1 and 2 find:
f (r + 1)
1. f (x) = 3-4x
2. f (x) = 8 - x - x^2
3. Graph the following functions:
f (x) = 2|x-3| - 4
4. A tree removal service assesses a $400.00 fee and then charges $80.00 per hour for the time on an owner's property
a. Is $750.00 enough for 5 hours of work.
b. Graph the ordered pairs (hours, cost). Give the domain and range.
5. Find the following for (Fixed cost is $2000.00; 36 units cost $8480.00).
The linear cost function
The marginal cost
The average cost per unit to produce 100 units
For questions 6 and 7 Graph each of the following quadratic functions, and label its vertex.
6. f(x) = 5 - 2x^2
7. f(x) = 5x^2 + 20x - 2
Use Graphing Calculator for question 8.
8. The average cost (in dollars) per item of manufacturing x thousand cans of spray paint is given by
A (x) = -.000006x^4 + .0017x^3 + .03x^2 - 24x + 1110
How many cans should be manufactured if the average cost is to be as low as possible? What is the average cost in that case?
9. The cost and revenue functions (in dollars) for a frozen - yogurt shop are given:
C(x) = (400x+400)/(x+4) and R(x) = 100x
Where x is measured in hundreds of units
Graph C(x) and R(x) on the same set of axes.
What is the break-even point for this shop?
If the profit function is given by P(x), does P(1) represent a profit or a loss?
Does P(4) represent a profit or a loss?
Please see the attached MS Word document for the full solutions to the questions. Included are charts, graphs, and written explanations.
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Functions and Graphs
8, 10, 16, 26, 30, 42, 46, 68, 78
For the functions in question 8 and 10 find:
f (r + 1)
8. f (x) = 3-4x
F(6)=3-4*6=-21; f(-2)=3-4*(-2)=11; f(p)=3-4p; f(r+1)=3-4(r+1)=-1-4r.
10. f (x) = 8 - x - x^2
F(6)=8-6-6^2=-34; f(-2)=8+2-(-2)^2=6; f(p)=8-p-p^2; f(r+1)=8-(r+1)-(r+1)^2=-r^2-3r+6
Graph the following functions:
16. f (x) = 2|x-3| - 4
26. A tree removal service assesses a ...
The functions using a graphing calculator is examined.
Sketching Graph Function Calculators
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