Download presentation

Presentation is loading. Please wait.

1
Lesson 3.8 Functions

2
**No input value is repeated so the relation is a function**

Definition A function is a special relation between values: The input value (domain) gives back exactly one unique Output value (range). Class Grade Function Student Grade 80 85 96 Bilal Peter Selma Ahmad George {(B, 85), (P, 96), (S, 80), (A, 85), (G, 96)} No input value is repeated so the relation is a function

3
**Example of a relation that is not a function**

Has visited Person Country Paris London Dubai New York Ahmed Rami Sally Nancy {(A, D), (A, P), (R, N), (S, P), (S, L), (S, D), (N, D)} The inputs A and S are repeated so the relation is not a function

4
**x y F(x) = x2 – 1 { } { } Function Notation (x2 – 1) function Domain**

{ } { } Domain 2, 5, 7, 10 Range 3, 24, 48, 99 F(x) = x2 – 1 Output input Function name

5
**F: x 3 – 2x; D = {0, 1, 2, 3} f(x) = 3 – 2x R = {3, 1, -1, -3} f(0) =**

Example The Domain D and the rule of some function are given. Find the range F: x – 2x; D = {0, 1, 2, 3} f(x) = 3 – 2x f(0) = 3 – 2(0) = 3 f(1) = 3 – 2(1) = 1 f(2) = 3 – 2(2) = -1 f(3) = 3 – 2(3) = -3 R = {3, 1, -1, -3}

6
**1) F(x) = x3 – 3 2) F(x) = Domain of the function**

The domain of a function is all the values that an input is allowed to take on. Give the domain of each function 1) F(x) = x3 – 3 There are no values that I can't plug in for x. when I have a polynomial, the answer is always that the domain is ”all real numbers” 2) F(x) = The only values that x can not take on are those which would cause division by zero. Here x can not take (1), so my domain will be “All real numbers except 1”

7
**3) F(x) = x – 2 ≥ 0 x ≥ 2 Domain of the function**

The only problem I have with this function is that I cannot have a negative inside the square root. So I'll set the insides ≥ 0, and solve. The result will be my domain: x – 2 ≥ 0 x ≥ 2 Then the domain is “all x ≥ 2”

8
**f(g(1)) f(g(1)) Composite functions**

Consider the functions: f(x) = 3x2 + 2 and g(x) = x + 1 is a composite function, where g is performed first and then f is performed on the result of g. The function fg may be found using a flow diagram Examples: find the indicated value: f(g(1)) f(g(1)) g(x) x + 1 f(x) 3x2 + 2 Method 1 1 input 2 input fg = 14 f(g(1)) Method 2 Step1: find g(1) = (1) + 1 = 2 Step2: find f(2) = 3(2)2 + 2 = = 14

9
H.W (4, 8, 12) + (30 – 40) Even page 144, 145

Similar presentations

OK

Real Zeros of Polynomial Functions Real Zeros of Polynomial Functions

Real Zeros of Polynomial Functions Real Zeros of Polynomial Functions

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google