1 / 9

2.6 Operations and Composition

2.6 Operations and Composition. Quiz. Let f(x) = 3x – 1, g(x) = x 2 -4, then (f + g)(x) = ______. (write the function expression ). Operations on Functions. Given two functions f and g, suppose Domain of f is D f , Domain of g is D g. Operations on Functions. Evaluate: (f+g)(6);

tien
Télécharger la présentation

2.6 Operations and Composition

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 2.6 Operations and Composition

  2. Quiz • Let f(x) = 3x – 1, g(x) = x2-4, then (f + g)(x) = ______. (write the function expression )

  3. Operations on Functions • Given two functions f and g, suppose Domain of f is Df, Domain of g is Dg

  4. Operations on Functions • Evaluate: (f+g)(6); • Find (fh)(x); • Find (g - f)(x). Is this the same as (f - g)(x)? • Find (g / h)(x) • Find (h - p)(x) • Evaluate: (h - p)(1); (h - p)(-4) f(x) = 3x -1 g(x) = x2 -4 h(x) = x + 2 p(x) = (x + 3)0.5

  5. Operations on Functions • Discussion 1, h(x) = x2 + 2x (a) Find h(x + 1) (a) Find h(x) + h(1) 2, f(x) = 3x + 5 (a) Find f(1/2) (b) Find f(1) / f(2)

  6. Operations on Functions • Example If possible, use the given representations of functions f and g to evaluate (f + g)(4), (f - g)(-2), (fg)(1), and (f/g)(0) f(x) = 2x + 1 g(x) = √ x Step 1: Find domains of f and g Step 2: Make sure the input is in the domain of f and g. If it is a quotient operation, make sure the denominator doesn’t equal to 0. Step 3: Find corresponding expressions of operations Step 4: Evaluate new generated functions

  7. Difference Quotients • Consider a nonlinear function f and draw a line through two points (x, f(x)) and (x + h, f(x + h)) y The slope of the line is: B = = y2 – y1 x2 – x1 f(x + h) – f(x) (x + h) - x f(x + h) – f(x) h A Difference Quotient x x x + h

  8. Difference Quotient • Example: Find and simplify the difference quotient for the function f given by f(x) = 3x2 + 2x

  9. Homework • PG. 144: 1-4, 12-21(M3), 24, 33, 36, 75, 77, 78 • KEY: 24, 36, 78 • Reading: 3.2 Quadratic Functions & Graphs

More Related