Download presentation
Presentation is loading. Please wait.
Published byEthel McCoy Modified over 8 years ago
1
Section 3.4 Library of Functions; Piecewise-defined Functions
2
Graph the Functions Listed in the Library of Functions
3
Constant Function xy=b -3 -2 0 1 2 3
4
Identity Function xy=x -3 -2 0 1 2 3
5
Square Function xy=x 2 -3 -2 0 1 2 3
6
Cube Function xy=x 3 -3 -2 0 1 2 3
7
Square Root Function xy=x 1/2 0 1 2 3 4 7 9
8
Cube Root Function xy=x 1/3 -27 -8 0 1 8 27
9
Reciprocal Function xy=1/x 4 4 2 1 1/2 1/3 1/4 0
10
xy=|x| -3 -2 0 1 2 3 Absolute Value Function
11
Greatest Integer Function x y= x -0.5 0 0.5 1 1.5 2
12
Piecewise-defined Functions
13
Use when x values satisfy condition n Use when x values satisfy condition 1 Sometimes we need more than one formula to specify a function algebraically. In this case the formula used to evaluate the function depends on the value of x. Piecewise Defined Functions
14
The following is a quick example of a piecewise defined function = 26.5 = 53.8 Use when x values are greater than 2 Use when x values are less than or equal to 2 Notice Example 1
15
Notice that the domain of f, in this case, is the set all real numbers. That is, Dom f = (– , ) The following is a quick example of a piecewise defined function Example 1
16
The percentage p (t) of buyers of new cars who used the Internet for research or purchase since 1997 is given by the following function.† (t = 0 represents 1997). Notice that the domain of p is the interval [0, 4]. That is, Dom p = [0, 4]. † The model is based on data through 2000. Source: J.D. Power Associates/The New York Times, January 25, 2000, p. C1 Example 2
17
This notation tells us that we use the first formula, 10t + 15, if 0 t < 1, or, t is in [0, 1) the second formula, 15t + 10, if 1 t 4, or, t is in [1,4] Example 2
18
Thus, for instance, p(0.5) = 10(0.5) + 15 = 20 Here we used the first formula since 0 0.5 < 1, or, equivalently, 0.5 is in [0, 1). p(2) = 15(2) + 10 = 40 We used the second formula since 1 2 4, or equivalently, 2 is in [1, 4]. p(4.1) is undefined p (t ) is only defined if 0 t 4. Example 2
19
The function f (x) is defined as Example 3
20
(a) (b) Example 4: Cost of Electricity
23
Therefore the function C (x) can be written as
Similar presentations
© 2024 SlidePlayer.com Inc.
All rights reserved.