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1. This slideshow will teach you everything you want to know about combining functions via products and quotients .

4. Finding Restrictions What is a restriction? A restriction is a value for a variable such as ‘x’ that would make the equal zero being undefined. Example Y=(x+4)(x-5) Sub and Solve x+4=0 Sub and Solve x-5=0 x=-4 x=5 Therefore the restrictions are 4 and 5. As if either value were inputted the one side would be multiplied against zero. We know zero multiplied by anything is equal to zero.

5. Finding Domain and Range What is Domain? Domain is the set of numbers for which a function is defined in terms of its x-values. A.K.A. All possible x-values for a given function. What is Range? Range is the set of numbers for which a function is defined in terms of its y-values. A.K.A. All possible y-values for a given function. Solve an Example y= (x+4) 2 (x+6) Or y= x 3 +14x 2 +72x+96 We know that the zeroes of the function would be -4 at an order of 2 and -6, these are the x-intercepts. Furthermore if the functions were multiplied together they would have a positive leading coefficient and is a cubic function. Therefore the function is extending upward in a positive manner from 3 to 1 thus the domain is XER and YER (ER= means element of the real number system.

6. Example Three: Quotient of a Function

7. Example Four: Word Problem A movie theatre decides to gradually reduce movie ticket prices after patrons to attract more. This can be modelled by the equation P(x)= 30-0.05m with m representing the movies being played since so far this year and p representing the price of tickets. Another part of the promotion is to give away free popcorn this can be modelled in terms of z by the equation Z(x)= 4-0.02m. After creating this promotion the number of attendees can be invited by the function N(x)=10+0.3m. Write a simplified equation to show the revenue from movie ticket sales. 1. Firstly we would choose to multiply equation p by n as p represents the price of tickets and n represents the number of movie-goers. Write this out. y= n(x)p(x) y= (10+0.3m)(30-0.05m) 2. Use the FOIL method (First Outside Inside Last) to solve the equation . Y=300-0.5m+9m+0.015 3. Simplify in order of degree. Y= 9.5m+300.015

8. And now you have learned section 8.2 Products and Quotients of Functions. For more help please refer to the examples and links on our Wiki.