<p>MHF4U Adding and Subtracting Functions</p><p>Functions can be added or subtracted from each other to form new functions. To do this you can either add both functions together algebraically, graphically or through a table of values. </p><p>Superposition principle – the sum of 2 or more functions can be found by adding the -coordinate of the functions for each -coordinate. </p><p>Applications in Physics - Wave Interference</p><p>Graph </p><p>Destructive Interference Constructive Interference</p><p>Example 1 Given and , determine a) b) c) </p><p>Example 2 Use the graph of and to sketch the graph of and .</p><p>Example 3 Investigating the Domain</p><p>Graph and . Then graph .</p><p>What is the domain of ?</p><p>In general, for two functions and , what is the domain of ?</p><p>Example 4 Given and a) Find the equation of </p><p> b) Find the equation of </p><p> c) Graph all 4 graphs. </p><p>Example 5 Given and , sketch the graphs of a) b) c) d) . ( and -intercepts accurate, but maximums and minimums not accurate) Example 6 Given and determine and graph: a)</p><p> b)</p><p>Example 7 Given and , Sketch a graph of a) b) c) d) State the domain of all 3 Example 8 The Profit Function The Athletic Council is selling T-shirts to raise money for new equipment. There is a fixed cost of $200 for producing the T-shirts, plus a variable cost of $5 per T-shirt made. Council has decided to sell the T- shirts for $8 each. a) Write an equation to represent i) The total cost, , as a function of the number, , of T-shirts produced</p><p> ii) The revenue, , as a function of the number, , of T-shirts produced.</p><p> b) Then, graph these functions on the same set of axes. Identify the point of intersection and explain the meaning of its coordinates.</p><p> c) Profit, , is the difference between revenue and expenses. Develop an algebraic and a graphical model for the profit function and graph it on the same grid as above.</p><p> d) Under what circumstances will the Athletic Council lose money? Make money?</p><p> e) Identify the domain and range of the cost, revenue, and profit functions in the context of this problem.</p>