Mathematics 30-1: Module 7 13 4. Oxalic acid is one of the finest available wood-bleaching agents. It is an acid, and the concentration used is critical to both safety and the bleaching result. Daulton plans to use the acid on a wood table to lighten dark streaks and colorations in the wood so that the wood will stain to a uniform colour. He finds two solutions in the workshop. Solution 1 has a concentration of 0.05 g/mL, and Solution 2 has a concentration of 0.01 g/mL. He starts with 150 mL of Solution 1, and he needs to add Solution 2 to get a final solution with a concentration of 0.025 g/mL. He uses the following formula to determine the amount of Solution 2 required. C (x)= amount of oxalic acid in Solution 1+ amount of oxalic acid in Solution 2 amount of Solution 1+ amount of Solution 2 For this question, after substituting known values, the following rational equation is obtained: 0.025 = (0.05)(150)+ 0.01x 150 + x Determine how much of Solution 2 needs to be added. (2 marks) 2012 Alberta EducationMathematics 30-1: Module 7 14 Lesson 4: Adding and Subtracting Functions 1. Let f(x) = x2 and g(x) = x + 4. a. State the function h(x) = f(x) + g(x). (1 mark) b. Graph the function h(x). (2 marks) 8 4 2 - 10 -8 -6 -4 4 $Mathematics 30-1: Module 7 15 2. Use the graphs of f(x) and g(x) to draw the graph of the following. State the domain and range for h(x) and p(x). 6 F ( X ) 9(x ) -4 6 x a. h(x) = (f+ g)(x) (3 marks) 6 F ( X ) 9(x ) 4 Domain Range 2012 Alberta EducationMathematics 30-1: Module 7 16 b. p(x) = (f-g)(x) (3 marks) 8- 6 F( X ) 9(X ) 2 4 Domain Range 3. Consider f(x) = x2 - 9, g(x) = 2x, and h(x) = 5x - 2. a. Determine p(x) = f(x) + 9(x) + h(x). (2 marks) b. Determine (x) = f(x) - g(x) - h(x). (2 marks)tathematics 30-1: Module 7 17 4. a. Is f(x) - g(x) = g(x) - f(x) true for all functions? (1 mark) b. Is (f + g)(x)= (g + f)(x) true for all functions? (1 mark) 5. Given f (x) = x and g(x) =x-5, a. Determine the equation of the function h(x) =(f -g)(x) (1 mark) b. Sketch the graphs of f(x), g(x), and h(x) on the same set of coordinate axes (3 marks) 10 -8 - 6 -4 c. State the domain and range of h(x) (2 marks)