College Algebra Functions

College Algebra Functions

Use this template to insert your answers for the assignment. Please use one of the four methods for showing your work (EE, Math Type, ALT keys, or neatly typed). Remember that your work should be clear and legible.

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible.

1. Is the following relation a function? Why or why not?

{(0, 1); (2, 6); (3, 4); (6, 1)}

Calculations:

Answer: ______

2. Is the following relation a function? Why or why not?

{(2, 3); (3, 3); (2, 4); (9, 4)}

Calculations:

Answer: ______

3. Given the function f(x) = 2x - 3, find three ordered pairs on the line.

Calculations:

Answer: ______

4. When f(x) = x2 + 2x - 5, find f(-3), f(0), and f(4).

Calculations:

Answer: ______

5. Rewrite the equation 5x – 7y = 15 as a function of x.

Calculations:

Answer: ______

In each of the following graphs, the bolded line represents a mathematical relationship between x and y. Use the vertical line test to determine whether the relationship is a function. Explain the reason for your conclusion.

6. / 7.

8. / 9.

6. Answer: ______

7. Answer: ______

8. Answer: ______

9. Answer: ______

The graph on the right represents the function .
10. What are the roots of the parabola?
Answer: ______
11. What is the domain of the function?
Answer: ______
12. What is the range of the function?
Answer: ______/

Evaluate the composite functions.

13. If f(x) = x+2 and g(x) = 3x+1, then find (f · g) (2).

Calculations:

Answer: ______

14. If f(x) = 2x-3 and g(x) = x+3, then find (g · f) (5).

Calculations:

Answer: ______

15. If f(x) = -5x+7 and g(x) = 3x-5, then find (f - g) (4).

Calculations:

Answer: ______

Second part

1. A rug company uses the following function to calculate the cost of producing throw rugs.

C(x)= 2.78x+23

If x represents the number of rugs, find the cost when 200 rugs are produced.

Answer: ______

2. A ball is dropped from a height of 65 feet and modeled by the following function

h(t)= -6t2 + 40t

If t represents the time in seconds after the ball is dropped, find h(5).

Answer: ______

3. The profit for selling cases of paper is represented by p(x)= 3.65x – 7.80. If x=2,000 and represents the cases of paper that are sold, find the profit.

Calculations:

Answer: ______

4. The time it takes a mechanic to complete an oil change is 7 minutes for each oil change and 10 minutes to set-up the station for the day. Write a function where x represents the number of cars that get an oil change. How long does it take to complete 50 oil changes?

Calculations:

Answer: Function: ______

Time after 50 oil changes: ______

5. An electrician charges a trip fee of $40 and $65 per hour. If h represents the number of hours he works on a job, write a function that represents this scenario. Calculate the cost of a job that runs for 7 hours.

Calculations:

Answer: Function______

Cost ______

6. The dosage (in mg) for Flea Alert is modeled by the function d(x) = 98x/18 where x represents the weight of the dog. Find the dosage for a dog that weighs 50 lbs. and a dog that weighs 14 lbs.

Calculations:

Answer: 50 lb. dog= ______

14 lb. dog= ______

What is the difference between a relation and function? Discuss how to find the domain and range of a function. What test can you use to identify a function on a graph? Explain how to use it.

Create your own function and solve the domain and range. Discuss the shape of the graph.