M. Flashman Fall '07

Operations and Composing Functions.

- Tools for Winplot used in this lab:

**Equation menu****explicit****Two****combinations**

Operations and Composing Functions

**End of Lab 12**

**Plot graphs with explicit for**

**y = p(x) = x^2****y = q(x) = x-3****y = h(x) =(x-3)^2**

**y = k(x) = x^2 - 3**

**Use Two combinations**

**use f + g with f = p and g = q to create x^2 + x - 3****use f - g with f = p and g = q to create x^2 - x + 3**

**[Note: This difference measures something graphically. What? when is it 0?]**

**use f * g with f = p and g = q to create x^2 ( x -3 )****When is this product 0?**

**use f / g with f = p and g = q to create x^2 /( x -3 )**

**When is this quotient 0? When is this quotient undefined?**

**use f <- g with f = p and g = q to create h(x)****When is this composition 0?**

**use f <- g with f = q and g = p to create k(x)****When is this composition 0?**

**Find p and q so that h(x) = q(p(x)) = sin(x^2).****Find p and q so that h(x) = p(q(x)) = (sin(x))^2****Find p and q so that h(x) = p(q(x)) = ln(x^2 +1)****Find p and q so that h(x) = p(q(x)) = (ln(x)^2) + 1**