1.5--Day 3--Arithmetic Combinations of Functions
What you should learn: To add, subtract, multiply, and divide
functions.
Just as two real numbers can be combined by the operations
of addition, subtraction, multiplication, and division to form
other real numbers, two functions cab be combined to create
new functions.
EX: Find the sum, difference, product, and quotient of f and g.
Sum:
Difference:
Product:
Quotient:
We can also evaluate arithmetic combinations of functions
at values.
EX: Given find
Two ways to find this.
Method One:
find f(2) and g(2)
subtract results
Method Two:
Find (f-g)(x)
then substitute 2 in
.
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EX: Evaluate the indicated function for EX: Find and what is the domain of ?
EX: Comparing Sales on Calculator
You own two restaurants. From 1990 to 1995, the sales R1(in thousands of dollars) for one restaurant can be modeled by R1 = 480 ­ 8t ­ 0.8t 2 t = 0, 1, 2, 3, 4, 5
where t = 0 represents 1990. During the same 6­year period, the sales R2 (in thousands of dollars) for the second restaurant can be modeled by R2 = 254 + 0.78t t = 0, 1, 2, 3, 4, 5.
a. Graph R1 and R2 on your calculator in Y1 and Y2.
b. Graph the function that represents the total sales for the two restaurants in Y3.
c. Use the new function for the total to estimate the total sales of the two restaurants in 2000.
HW: p. 169 19­29 odd, 33­37 odd, 48 = 10 problems
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