Domain and Range

Domain The domain is the set of all x values that work in the function To find the domain: – What kind of numbers can I plug in for x?? Positive numbers?? Negative numbers?? Zero??

Range The range is the set of all y values that a function outputs To find the range: – you have to think!! what numbers can you get out of the function??

Polynomials f(x) = -2x 4 – 6x g(x) = 2x + 1 y = (x – 9) 2 D: All Real Numbers

Absolute Value f(x) = |x – 2| g(x) = 3|2x – 1| y = -4 |x + 1| + 3

Radical Functions

Rational Functions

1.5 Combinations of Functions

Arithmetic Combinations of Functions Sum: (f + g)(x) = f(x) + g(x) Difference: (f – g)(x) = f(x) – g(x) Product: (fg)(x) = f(x) · g(x) Quotient:

Find the sum, difference, product, and quotient of the two functions. 1.f(x) = 2x + 1 g(x) = x 2 + 2x – 1 2. f(x) = x 2 g(x) = x – 3 3.

Compositions of Functions The composition of the function f with the function g is: The domain of f ᵒ g is the set of all x in the domain of g such that g(x) is in the domain of f

Finding compositions of functions and their domains Find and then their domains 1. 2.

Identifying a Composite function Write h(x) as a composition of two functions 1.h(x) = (3x – 5) 3 2.

Bacteria Count The number N of bacteria in a refrigerated food is given by where T is the temperature of the food in degrees Celsius. When the food is removed from the refrigeration, the temperature of the food is given by where t is time in hours. a.Find the composition N(T(t)) and interpret its meaning b.Find the number of bacteria in the food when t = 2 hours c.Find the time when the bacterial count reaches 2000.

Combinations of functions using a graph