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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)}
2. Is the following relation a function? Why or why not?
3. Given the function f(x) = 2x - 3, find three ordered pairs on the line.
4. When f(x) = x2 + 2x - 5, find f(-3), f(0), and f(4).
5. Rewrite the equation 5x – 7y = 15 as a function of x.
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.
10. What are the roots of the parabola?
The roots are the x-values where the graph crosses the x-axis. These points occur at x = -2 and x = 3.
11. What is the domain of the function?
The domain is the set of x-values that appear on the graph. For this parabola, any x-value will have a corresponding point on the graph. The domain then consists of the interval from negative infinity to positive infinity.
12. What is the range of the function?
13. If f(x) = x+2 and g(x) = 3x+1, then find (f · g) (2).
14. If f(x) = 2x-3 and g(x) = x+3, then find (g · f) (5).
15. If f(x) = -5x+7 and g(x) = 3x-5, then find (f - g) (4).
1. A rug company uses the following function to calculate the cost of producing throw rugs.
2. A ball is dropped from a height of 65 feet and modeled by the following function
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.
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?
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.
6. The dosage (in mg) for Flea Alert is modeled by the function 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.
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.
