3.6-1 Combining Functions

• If we have multiple functions, we can combine them/evaluate them at values, to produce a single value

• The combination can be produced by just using numbers

Addition/Subtraction

• Let f and g be two functions• A) (f + g) (x) = f(x) + g(x)– Ex. (f + g) (1) = f(1) + g(1)

• B) (f – g) (x) = f(x) – g(x) – Ex. (f – g) (-1) = f(-1) – g(-1)

Multiplication/Division

• Let f and g be two functions• C) (fg) (x) = f(x)g(x)– Ex. (fg) (-3) = f(-3)g(-3)

• D) (f/g)(x) = f(x)/g(x)– Ex. (f/g)(5) = f(5)/g(5)

• We do not necessarily need to know the actual function

• We just need to know the function values for f(x) and g(x)– Graphs– Sets of ordered pairs– Function itself– Values for f(x) and g(x)

• Example. Given that f(-3) = 15 and g(-3) = -4, find:• 1) (f + g)(-3)

• 2) (f – g)(-3)

• 3) (fg) (-3)

• 4) (f/g)(-3)

• Example. Given the following, find (fg)(-3) and (f + g)(-3).

• f = {(1, -3), (-3, 5), (6, 10), (4, 4)}• g = {(2, 6), (-3, 9), (1, 11), (12, -3)}

Finding Formulas

• If we need to find a new formula, we simply will look to combine the functions using the correct operation– Distribute– Check for properties of exponents– Combine like terms

• Example. Find the formula and domain for (f + g) and (f/g) given the following two functions.

• f(x) = x – 3• g(x) = x2

• Example. Evaluate (f + g)(10) and (fg)(1) given the following two functions.

• f(x) = 1/x2

• g(x) = 2x + 3

• Assignment• Pg. 269• 1-29 odd