By Chris Kirkpatrick, Marian Small, Barbara Alldred

Built for the ON Grade 12 complicated features Curriculum MHF4U, Revised 2007. good points & merits include:

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• a number of solved examples with motives combine the mathematical process

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**Sample text**

Draw a smooth curve through the points since the function is continuous. 0 8 To graph radius in terms of volume, switch the variables in the table, making radius the dependent variable and volume the independent variable. 6 4 2000 4000 6000 Volume (cm3) 16 y 12 y=x 8 4 –4 0 –4 The red curve shows volume as the independent variable and radius as the dependent variable. 4 8 12 16x If we ignore units and plot both relations on the same graph, the red curve is a reflection of the blue curve in the line y 5 x.

A popular coffee house sells iced cappuccino for $4 and hot cappuccino for $3. The manager would like to predict the relationship between the outside temperature and the total daily revenue from each type of cappuccino sold. The manager discovers that every 1 °C increase in temperature leads to an increase in the sales of cold drinks by three cups per day and to a decrease in the sales of hot drinks by five cups per day. 150 y f(x) = 3x+10 100 50 –10 0 The function g(x) 5 25x 1 200 can be used to model the number of hot cappuccinos sold.

Do you have to restrict either the domain or the range of the function y 5 "x 1 2 to make its inverse a function? Explain. 16. John and Katie are discussing inverse relationships. John says, C “A function is a rule, and the inverse is the rule performed in reverse order with opposite operations. For example, suppose that you cube a number, divide by 4, and add 2. ” Is John correct? Justify your answer algebraically, numerically, and graphically. Extending 17. f (x) 5 x is an interesting function because it is its own inverse.