Operations on Functions

Function Operations

• Multiplication of Functions: This operation combines two functions by multiplying them together, denoted as ( (f \cdot g)(x) = f(x) \cdot g(x) ).
• Division of Functions: This operation involves dividing one function by another, represented as ( (f / g)(x) = f(x) / g(x) ).
• Addition of Functions: This operation combines two functions by adding them together, expressed as ( (f + g)(x) = f(x) + g(x) ).

Parent Function

• Parent Function: Refers to the most basic form of a function, often represented by simple polynomial, trigonometric, or exponential functions, such as (f(x) = x).

Transformations of Specific Functions

• Action of (B) on (F(x) = |x|): The action implies a transformation, typically affecting the graph's symmetry or orientation, possibly involving stretching or compressing the absolute value function.
• Action of (D) on (F(x) = x^3): This action modifies the cubic function, potentially altering its domain or range, which can affect its inflection points and overall shape.
• Action of (C) on (F(x) = \sin(x)): This transformation may adjust the amplitude or period of the sine wave, influencing how many cycles occur over a given interval.
• Action of (A) on (F(x) = e^x): This action typically modifies the exponential growth behavior, potentially shifting the graph up, down, or altering the base of the exponential function.

Test your knowledge on operations on functions including multiplication, division, addition, and subtraction. Learn which operation combines two functions by multiplying them together, dividing one function by another, or adding them together.