3.2 Notes Alg1 LH.notebook October 23, 2012
1. Write a possible situation for the given graph.
2. A pet store is selling puppies for $50 each. It has 8 puppies to sell. Sketch a graph for this situation.
3. Generate ordered pairs for the function y = x + 3 for x = –2, –1, 0, 1, and 2. Graph the ordered pairs.
(2,_____)(1, ____)etc
Skills we've learned
Skills we need
3.2 Relations and Functions
2. A pet store is selling puppies for $50 each. It has 8 puppies to sell. Sketch a graph for this situation.
3. Generate ordered pairs for the function y = x + 3 for x = –2, –1, 0, 1, and 2. Graph the ordered pairs. (2, 1)(1, 2)
(0, 3)(1, 4)(2, 5)
Warmup Answers
3.2 Notes Alg1 LH.notebook October 23, 2012
How to Graph a Point...
10 2 3 4 5 6 7 8 9 1012345678910
one dimension:
two dimensions:
3.2 Notes Alg1 LH.notebook October 23, 2012
3.2 Notes Alg1 LH.notebook October 23, 2012
3.2 Relations and Functions
Identify functions. Find the domain and range of
relations and functions.
In the scoring systems of some track meets, for first place you get 5 points, for second place you get 3 points, for third place you get 2 points, and for fourth place you get 1 point. This scoring system is a relation, so it can be shown by ordered pairs. {(1, 5), (2, 3), (3, 2) (4, 1)}
I. Multiple Representations of Relations
1.
3.2 Notes Alg1 LH.notebook October 23, 2012
Domain and Range
ps... they are ALL in Alpha Order sweet! :)
DOMAIN RANGE
{(1, 5), (2, 3), (3, 2) (4, 1)}
(first, second)Input Output x yxaxis yaxis
II. Finding the Domain and Range of a Function
The range value is all yvalues from 3 through 4, inclusive.
The domain value is all xvalues from 1 through 5, inclusive.
The domain value is all xvalues 1, 2, 5 and 6.
The range value is all yvalues 0, –1 and –4.
Domain: {6, 5, 2, 1}
Range: {–4, –1, 0}
The range values are yvalues 1 and 4.
Domain: {1, 4, 8}Range: {1,4}
The domain values are all xvalues 1, 4, and 8.
2.
3.
4.
3.2 Notes Alg1 LH.notebook October 23, 2012
III. Identifying Functions
5. Give the domain and range of the relation. Tell whether the relation is a function. Explain.
Even though 3 is in the domain twice, it is written only once when you are giving the domain.
D: {3, 5, 4} R: {–2, –1, 0, 1}
The relation is not a function. Each domain value does not have exactly one range value. The domain value 3 is paired with the range values –2 and 1.
{(3, –2), (5, –1), (4, 0), (3, 1)}
A function is a special type of relation that pairs each domain value with exactly one range value.
Answer
Give the domain and range of the relation. Tell whether the relation is a function. Explain.
D: {4, 8, 4, 5} R: {2, 1} This relation is a function. Each domain value is paired with exactly one range value.
Use the arrows to determine which domain values correspond to each range value.
6.
3.2 Notes Alg1 LH.notebook October 23, 2012
Domain:Range:Function?
7.
Give the domain and range of the relation. Tell whether the relation is a function. Explain.
D: –5 ≤ x ≤ 3 R: –2 ≤ y ≤ 1
The relation is not a function. Nearly all domain values have more than one range value.
Draw lines to see the domain and range values.
8.
IV. Identifying Functions with Graphs
3.2 Notes Alg1 LH.notebook October 23, 2012
Give the domain and range of the relation. Tell whether the relation is a function. Explain.
{(8, 2), (–4, 1), (–6, 2),(1, 9)}
10. 11.
D: {–6, –4, 1, 8} R: {1, 2, 9} The relation is...
a function. Each domain value is paired with exactly one range value.
D: {2, 3, 4} R: {–5, –4, –3}
The relation is...
not a function. The domain value 2 is paired with both –5 and –4.
Domain:Range:Function?
9.
3.2 Notes Alg1 LH.notebook October 23, 2012
3.2 p.173 #5, 7, 9 21, 24 28, 32 36*25 problems
SA6
In 30 minutes we will begin 3.3
3.3 Preview: Function Notation
x f(x)
10123
3.2 Notes Alg1 LH.notebook October 23, 2012
3.3 Preview: Function Notation
1. Let f(x) = x + 5, find
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