Name: Algebra 1 Section 3 Homework Problem Set: Introduction to Functions Remember: To receive full credit, you must show all of your work and circle/box your final answers. If you run out of room for work, please use a piece of notebook paper. 1. Determine whether the following relations are functions by writing function, or not a function below the representation. (there are 12 different relations to determine) Domain Range Domain Range
2. Find the range of the functions given the domain. a. f(x) = x 2 3x + 2; Domain: { 3, 1,2}. b. g(x) = 2 x + 5; Domain: { 1,11,31}. c. h(x) = 2 x + 5 ; Domain: { 9, 7, 2}. d. k(x) = 3 2 x+1 10; Domain { 1,1,2,3}. 3. A giraffe s hunger level depends on the size of its last meal. Part A: What is the independent variable? Part B: What is the dependent variable? 4. You earn $20 per hour doing landscaping work. Your total earnings depend on the amount of hours you spend landscaping. Part A: What is the independent variable? Part B: What is the dependent variable? Part C: Write a function to represent the situation.
5. Perform the following operations with the functions. f(x) = 6x 2 g(x) = x 2 5x + 4 h(x) = 5x 2 + x + 7 k(x) = 7 3x a. g(x) + h(x) b. f(x) k(x) c. f(x) h(x) d. g(x) k(x) e. h(x) g(x) f. f(k(x)) 6. Consider the following functions that represent cost and revenue for a band s sales of spirit mugs, if they decide to sell the mugs for $8 each. a. Which function represents the cost function? f(x) = 100 + 3x g(x) = 8x b. Which function represents the revenue function? c. Write the profit function. d. What s the profit if 400 spirit mugs are sold?
7. Perform the following operations with the functions. f(x) = 3x 1 g(x) = 8x 2 + 5x 3 h(x) = 2x 2 x 6 k(x) = 5 + 2x a. g(x) + h(x) b. f(x) k(x) c. g(x) k(x) d. h(x) f(x) e. h(x) g(x) f. k(f(x)) 8. The student government association is selling roses for Valentine s Day to raise money for their trip to the state convention. The cost of each rose is $1. 50 and the florist charges a delivery fee of $25. The class plans to sell the roses for $5. 00 each. a. Write a cost function C(x). b. Write a revenue function R(x). c. Write a profit function P(x). d. What s the profit if 200 roses are sold?
9. Floyd drinks two Mountain Dew sodas in the morning. The function that represents the amount of caffeine, in milligrams, remaining in his body after drinking the sodas is given by f(t) = 110(0. 8855) t where t is time in hours. Floyd says that in two days the caffeine is completely out of his system. Do you agree? Justify your answer. 10. Natural numbers {1, 2, 3, 4, 5, 6.. } are not closed under subtraction. Give an example of why they are not, and explain. 11. Negative integers {.. 6, 5, 4, 3, 2, 1} are not closed under multiplication. Give an example of why they are not, and explain. 12. Identify the key features of the following graphs. a. Domain Range Increasing Decreasing Maximum x-intercepts y-intercept
b. Domain Range Increasing Decreasing Minimum x-intercept y-intercept c. Domain Range Increasing Decreasing Maximum x-intercept y-intercept
d. Domain Range Increasing Decreasing Minimum x-intercepts y-intercept 13. Consider the graph to the right. Which of the following statements are true? Select all that apply. The graph is increasing when x < 2. The graph has a relative minimum at (0, 0). The graph has two relative maximums. The graph is decreasing when [ 2 < x < 0] [2 < x < 7]. The domain is 6 < x 7. The range is x 4.
14. The table below shows the values for the function f(x). x -4-1 0 2 3 f(x) 12 6 4 8 10 a. Complete the table for the function 1 2 f(x) + 2. b. Complete the table for the function 2f(x) 3 x -4 1 f(x) + 2 2 x -4 2f(x) 3-1 -1 0 0 2 2 3 3 15. The table below shows the values for the function g(x). x -6-2 0 1 2 g(x) -3 0 6 15 30 a. Complete the table for the function 2g(x) + 5. b. Complete the table for the function 1 3 g(x) 1 x -6 2g(x) + 5 x -6 1 g(x) 1 3-2 -2 0 0 1 1 2 2
16. Perform the following shifts on the functions. a. Describe the shift, then graph the functions g(x) and h(x). g(x) = f(x + 4) + 1 h(x) = f(x 1) 6 b. Describe the shift, then graph the function n(x) and p(x). n(x) = m(x + 2) 5 p(x) = m(x 3) + 4
17. Consider the table below for the function f(x) = 2 x. Point x f(x) a. Find the average rate of change over the interval [C,E] A 0 1 B 1 2 b. Find the average rate of change over the interval [B,F] C 2 4 c. Find the average rate of change over the interval [A,F] D 3 8 E 4 16 d. Find the average rate of change over the interval [E,H] F 5 32 G 6 64 e. Find the average rate of change over the interval [F,H] H 7 128 18. Consider the graph of the function below. a. Find the average rate of change over the interval [B,C] b. Find the average rate of change over the interval [C,D] c. Find the average rate of change over the interval [D,E] d. Find the average rate of change over the interval [A,C]