3.6-1 Combining Functions

1. 3.6-1 Combining Functions

2. 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

3. 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)

4. 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)

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)

6. 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)

7. 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)}

8. 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

9. Example. Find the formula and domain for (f + g) and (f/g) given the following two functions. • f(x) = x – 3 • g(x) = x2

10. Example. Evaluate (f + g)(10) and (fg)(1) given the following two functions. • f(x) = 1/x2 • g(x) = 2x + 3

11. Assignment • Pg. 269 • 1-29 odd