Operations on Functions Composite Function Operations Notation Sum

  • Slides: 14
Download presentation
Operations on Functions Composite Function: Operations Notation: Sum: Difference: Product: Quotient: Combining a function

Operations on Functions Composite Function: Operations Notation: Sum: Difference: Product: Quotient: Combining a function within another function. Written as follows:

Example 1 a) Add / Subtract Functions b)

Example 1 a) Add / Subtract Functions b)

Example 2 a) Multiply / Divide Functions b)

Example 2 a) Multiply / Divide Functions b)

Example 3 Evaluate Composites of Functions Recall: (a + b)2 = a 2 +

Example 3 Evaluate Composites of Functions Recall: (a + b)2 = a 2 + 2 ab + b 2 a) b)

Example 4 a) Composites of a Function Set

Example 4 a) Composites of a Function Set

Example 4 b) Composites of a Function Set

Example 4 b) Composites of a Function Set

Inverse Functions and Relations Inverse Relation: Inverse Notation: Inverse Properties: 1] 2] Relation (function)

Inverse Functions and Relations Inverse Relation: Inverse Notation: Inverse Properties: 1] 2] Relation (function) where you switch the Domain and range values

Steps to Find Inverses [1] Replace f(x) with y [2] Interchange x and y

Steps to Find Inverses [1] Replace f(x) with y [2] Interchange x and y [3] Solve for y and replace it with One-to-One: A function whose inverse is also a function (horizontal line test) Inverse is not a function

Example 1 a) b) Inverses of Ordered Pair Relations

Example 1 a) b) Inverses of Ordered Pair Relations

Inverses of Graphed Relations The graphs of inverses are reflections about the line y=x

Inverses of Graphed Relations The graphs of inverses are reflections about the line y=x

Example 2 a) Find an Inverse Function b)

Example 2 a) Find an Inverse Function b)

Example 2 c) Continued d) Inverse is not a 1 -1 function. (BUT the

Example 2 c) Continued d) Inverse is not a 1 -1 function. (BUT the inverse is 2 different functions: If you restrict the domain in the original function, then the inverse will become a function.

Example 3 a) Verify two Functions are Inverses Method 1 b) Method 2 Yes,

Example 3 a) Verify two Functions are Inverses Method 1 b) Method 2 Yes, Inverses

Example 4 One-to-One (Horizontal Line Test) Determine whether the functions are one-to-one. a) b)

Example 4 One-to-One (Horizontal Line Test) Determine whether the functions are one-to-one. a) b) One-to-One Not One-to-One