02Hwrkshtsolns

Worksheet: Combination Graphs

Solutions

a) Sketch the __**sum function**__ y = f(x) + g(x), where math \\ f(x)=\dfrac{1}{x+2} \quad \text{ and } \\ \\ g(x)=-2x-1 math

Domain: x Î **R**\{–2} Range: y Î **R**

Asymptotes x = –2 y = –2x – 1

No turning points

y-intercepts: y = –0.5 x-intercepts: x = –2.28, –0.22

b) Sketch the __**difference function**__ y = f(x) – g(x) where

math \\ f(x) = x^2-3 \quad \text{ and } \\ \\ g(x) = |2x+1|-2 math

Domain: x Î R Range: y ≽ –3

No asymptotes

Turning Points Local minimum: (1, –3) Local minimum: (–1, –1) Local maximum: (–0.50, –0.75)

y-intercept: y = –2 x-intercepts: x = –2, 2.73

c) Sketch the product function y = f(x) × g(x) where math \\ f(x) = 2 \sqrt{x+3}-1 \\ \text{and} \\ g(x) =x-1 math

Domain: x ≽ –3 Range: y ≽ –3.70

No asymptotes

Endpoint at (–3, 4)

Turning points: Minimum at (–1.22, –3.70)

y-intercept: y = –2.46 x-intercepts: x = –2.75, 1

Return to Combination Graphs Worksheet

Return to Sum, Difference and Product Graphs

.