1.5A Combination Functions 1. Sum (f + g)(x) = f(x) + g(x) Add like terms of the 2 functions. 2. Difference (f – g)(x) = f(x) – g(x) Subtract like terms of the 2 functions. 3. Product (fg)(x) = f(x) • g(x) Multiply (distrib., FOIL, etc.) and simplify (combine like terms). 4. Quotient ( 𝒇 𝒈 )(x) = 𝒇(𝒙) 𝒈(𝒙) 𝒈 𝒙 ≠𝟎 Set up division and simplify if possible.

Domains of Combination Functions The domain of the combination function is all real numbers that are COMMON TO (shared by) the domains of each function. The domain of a combination function with a quotient is the shared domain where denominator ≠ 0.

Combination Functions in the Calculator y₁ = function f y₂ = function g y₃ = combination function (use symbols y₁ & y₂ when entering) Vars → y-vars 1: function & choose desired function name

Evaluating combinations with calculator Enter all 3 functions in y= (use VARS for y₃) 2nd , TRACE, 1:value Enter desired value & enter Use up & down arrows to view value on all 3 functions.

Examples 1. Graph h(x) = (f + g) (x)

More examples 2. f(x) = x + 3 g(x) = x – 3 Find: A) (f + g)(x) B) (f – g)(x) C) (fg)(x) D) (f/g)(x) E)Domain of (f/g)(x)

More Examples 3. f(x) = x²- 1 g(x) = x – 2 A.) Evaluate (f + g)(3) algebraically B) Evaluate (f + g)(3) with the calculator.

More Examples 4. f(x) = 3x g(x) = - 𝑥³ 10 A.) graph f(x) , g(x) and (f + g)(x) in calculator. B. Which function contributes most to the magnitude of the sum when 0≤x≤2? C. Which function contributes most to the magnitude of the sum when x > 6?