Questions

IB MATH METHODS

MATHEMATICAL INVESTIGATION

PROJECT #1

Given F(x) = x² , Investigate the behavior of the function as you answer the following questions:

In questions 1 through 2 assume that d is a positive number.

1. How is the graph of y = f(x) + d related to y = f(x)?

2. How is the graph of y = f(x) – d related to y = f(x)?

In questions 3 through 4 assume that c is a positive number

3. How is the graph of y = f(x + c) related to y = f(x)?

4. How is the graph of y = f(x - c) related to y = f(x)?

5. How is the graph of y = -f(x) related to y = f(x)?

6. How is the graph of y = f(-x) related to y = f(x)?

In questions 7 through 8 assume that a is a positive number

7. If a>1, how does y = af(x) compare with y = f(x)?

8. If 0<a<1, how does y = af(x) compare with y = f(x)?

In questions 9 through 10 assume that b is a positive number

9. If b>1, how does y = f(bx) compare with y = f(x)?

10. If 0<b<1, how does y = f(bx) compare with y = f(x)?

11. Generalize your findings to other types of functions such as cubic, square root, reciprocal. Give a rational for your generalization