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.