Combination of Functions Lesson 8.3

Functions to Combine Enter these functions into your calculator

Combining Functions Consider the following expressions Predict what will be the result if you graph

Combining Functions Turn off the two original functions (F4) Use them in the expression for the combined function How does this differ from a parabola?

Application Given two functions having to do with population  P(x) is the number of people  S(x) is the number of people who can be supplied with resources such as food, utilities, etc. Graph these two functions  Window at 0 < x < 100 and 0 < y < 1000

Population and Supply Viewing the two functions  Population  Supply What is the significance of S(x) – P(x) What does it look like – graph it

Population and Supply What does it mean? When should we be concerned?

Population and Supply Per capita food supply could be a quotient When would we be concerned on this formula? Set window -5 < y < 5

Combinations Using Tables Determine the requested combinations x r(x) s(x) s(x)/r(x) r(x)-s(x) 4 – 2r(x)

Descriptive Functions Let f(t) = number of males, g(t) = number of females in Canada in year t Let h(t) = average income of females in Canada in year t What is the formula for p(t)  The number of people in Canada in year t What is the formula for m(t)  The total amount of money earned by Canadian females in year t

Simplifying Formulas Given functions Write simplified formulas for  f(x) = u(x) + v(x)  k(x) = v(x) 2  h(x)=2u(x) – 3v(x)

Assignment Lesson 8.3 Page 379 Exercises 1 – 41 EOO