Math 115  Lab #12
M. Flashman Fall '07

Operations and Composing Functions.
• Tools for Winplot used in this lab:
• explicit
• Two
• combinations

Operations and Composing Functions
• 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

End of Lab 12