EXPLORING FINITE DIFFERENCES II

QUESTIONS

1. Do the following with the x step set at 1 and a = 0 so that you have a linear function.

a)   What is the relation between b and the first differences ?

b) How does changing the value of c affect the first differences ?

2. Change the x step value to 2, leaving a = 0 .

What are the answers to 1a) and 1b) now ?

3.  By varying the x step value and the b value, make a general conclusion :

For a linear function y = bx + c and an x step value of k,  the first difference will always be ________ .

4. Prove this is true by letting f(x) = bx + c and evaluating f(x + k) – f(x).

5. To investigate quadratics, begin by setting a = 1 with the x step value set at 1.

Now the first differences are not the same –  it is the second differences which

are equal.

6. How does changing the values of a, b and c affect the second differences ?

7. Change the x step value. Now how do the second differences change ?

8. Complete the following general statement :

For a quadratic function y = ax2 + bx + c and an x step value of k, the second difference will always be ___________ .

9. Prove this result is true by letting f(x) = ax2 + bx + c. Use the following as a guide.

 1st difference 2nd difference x f(x) x + k f(x + k) f(x + k) – f(x) x + 2k f(x + 2k) f(x + 2k) – f(x - k) [f(x + 2k) – f(x - k)] – [f(x + k) – f(x)]