Download presentation
1
Section 1.2 Basics of Functions
2
Definition of a Relation
Math Section 1.2 Definition of a Relation A relation can be expressed as a set of ordered pairs. The domain of a relation is the set of first elements in the ordered pairs, and the range is the set of second elements. Relation: {(0 , 5), (2 , 1), (2 , 1), (3 , 8)} Domain: {0, 2, 3} Range: {5, 1, 1, 8} Relation: {(0 , 5), (2 , 1), (2 , 1), (3 , 8)} Domain: {0, 2, 3} Relation: {(0 , 5), (2 , 1), (2 , 1), (3 , 8)}
3
Example Find the domain and the range.
4
Definition of a Function
Math Section 1.2 Definition of a Function A function is a relation for which each element of the domain corresponds to exactly one element of the range. Relation: {(0 , 5), (2 , 1), (2 , 1), (3 , 8)} Function: {(0 , 2), (1 , 8), (5 , 2), (1 , 3)} In other words, no x coordinate can be paired with more than one y coordinate. 1 8
5
Example Determine whether each relation is a function?
6
Function Notation
7
A function can also be expressed as an equation.
Math Section 1.2 Function Notation A function can also be expressed as an equation. f(x) = x2 + 5x 2 “f of x” f(3) = (3) 2 = 22 f(1) = (1)2 + 5(1) 2 = 6 f(z+2) = (z+2)2 + 5(z+2) 2 = z2 + 4z z + 10 2 = z2 + 9z + 12
8
Example Evaluate each of the following.
9
Example Evaluate each of the following.
10
Example Evaluate each of the following.
11
Graphs of Functions
12
x f(x)=-2x (x,y) g(x)=-2x+3 -2 f(-2)=4 (-2,4) g(-2)=7 (-2,7) -1
(-1,2) g(-1)=5 (-1,5) f(0)=0 (0,0) g(0)=3 (0,3) 1 f(1)=-2 (1,-2) g(1)=1 (1,1) 2 f(2)=-4 (2,-4) g(2)=-1 (2,-1) See the next slide.
13
g(x) f(x)
14
Example Graph the following functions f(x)=3x-1 and g(x)=3x
15
The Vertical Line Test
16
The first graph is a function, the second is not.
17
Example Use the vertical line test to identify graphs in which y is a function of x.
18
Example Use the vertical line test to identify graphs in which y is a function of x.
19
Obtaining Information from Graphs
20
Example Analyze the graph.
21
Identifying Domain and Range from a Function’s Graph
22
Math Section 1.2 The domain of a function is the set of all x values for which the function is defined. Domain x2 4 0 x 2, 2 ( , 2) (2 , 2) (2 , ) Domain 2x + 6 0 2x 6 x 3 [3 , )
23
Math 112 Section 1.2 Finding the Domain & Range of a Function
The domain of a function is the set of all x values from the graph. The range of a function is the set of all y values from the graph. Domain: ( , ) Range: [1 , )
25
Example Identify the Domain and Range from the graph.
26
Example Identify the Domain and Range from the graph.
27
Example Identify the Domain and Range from the graph.
28
Identifying Intercepts from a Function’s Graph
29
Example Find the x intercept(s). Find f(-4)
30
Example Find the y intercept. Find f(2)
31
Example Find the x and y intercepts. Find f(5).
32
Find f(7).
33
Find the Domain and Range.
35
Example Determine whether each equation defines y as a function of x.
Similar presentations
© 2024 SlidePlayer.com Inc.
All rights reserved.