1. Are all relations functions? If not, give a counterexample.
For numbers 2 and 3, use the following table:
2. Is y a function of x? Justify your answer.
3. Is x a function of y? Justify your answer.
4. Researchers at UNC have determined that the number of mathematics students who suffer from "panic headaches" while taking an in-class test depends on the number of word problems on the test. Last semester, observations yielded the following data:
a) Write a linear equation which shows the relationship between the number of word problems and the number of students who had headaches.
b) Use your equation from a) to compute how many students had headaches if a test contained four word problems.
5. Write f(x) = x^2 + 6x + 15 in completed square form. Then sketch its graph.
For numbers 6-9, describe the relationship between the graph of f and the graph of g.
6. f(x) = (3/4)^x , g(x) = (3/4)^x - 2
7. f(x) = 2^x , g(x) = 2^(x-5)
8. f(x) = 3.9^x , g(x) = -3.9^x
9. f(x) = 5^x , g(x) = 5^(x+2) - 5
For numbers 10-16, describe and classify each function. (Describe means to find the center, asymptotes, vertex, y-intercept, slope, if it opens up or down, etc. appropriate to each particular function. Classify means to tell if the function is linear, quadratic, or rational.)
10. f(x) = x^2 + 10x + 27
11. f(x) = (2x + 3)/(x + 1)
12. f(x) = 4x + 3
13. f(x) = -3x -1
14. f(x) = -3/(x - 1) - 2
15. f(x) = (1/2)x^2 - 10x + 55
16. f(x) = -3x^2 + 42x -151