Identify Discrete andContinuous Functions,J,qAt Groph and classify discrete and continuous functions.

Key VOCabularv• discrete function• continuousfunction

The gr(tp!) of it funetlnn can consist of individual points, as in tile graph inExample 3011 page 207. The graph of a function can also be a line or a parrof a line with no breaks, as in the ~\'aph in Example 4 on page 217,

"," KEY CONCEPT - 'For Your-Notebook ;"" ,

tr: Identifying Discrete and Continuous Functions

','~ Adiscrete Junction has a graph Acontinuous function has a~~ ihar consists oflsolared points. graph that is unbroken.t~J:t~1:f~t

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\1iEli!Vl;Ug Graph and classify a function ~ ' _

Graph the function y '" 2x - 1 with the given domain. Classify the functionas discrete or continuous.

a. Domain: x = O, 1,2.3 b. Domain: x;;' 0

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The graph consists of individualpoints. so the function is discrete.

The graph is unbroken, sothe function is continuous.

GRAPHS As a general rule, you can tell that a function is continuous if yon donot have to lift your pencil from the paper to draw its graph. as ill part rb) ofExample I.

__ .(Ia!i~i!r••lId gt!J!h ~ r.e.•••J~world~i1.!tion _

Tell whether the function represented by the table is discrete orcontinuous. Explain. If continuous, graph the function and find thevalue ofywben x = 1.5.

Duration of storm th(J\.ws}, x 2 3

Amoumofraint;nthe~i,y 0.5 '1.5-----"'----_. -' ---~-'-.. _. -_. _._---- ---

solutionAlthough the table shows the amount ofrain (hut has fallen alter whole numbers ofhours only. it makes sense to talk about theamount of rain after any amou nt of timeduring the storm. So. the table represents acontinuous function.

The graph of the function is shown. To findthe value ufy when x = 1.5, start at 1.5 onthe .c-axis, move up to the graph. and moveover to the j-uxis, The y-value is about 0.75.So. about 0.75 inch of rain has fallen afterl.5 hours.

on p. 223for EX5. 1-6 1. Y = -2x + 3; domain: -2. -1. 0, 1. 2

Graph the function with the given domain, Classify the function as discreteor continuous.

EXAMPLE 1.......... ~., ~~~~

2. J' = .r: domain: ail real numbers

3. r= -tX'1'" 1;domain: -12, -6,0,6,12

5. .v = 3x - 4; dumain: x s: 0

4. Y= O.S.\:;domain: -2. -1. 0.1. 2

6• .v = ~x + t: domain: x ~-2

_~~.~.~,!,:~.~..~.... Tell whether the function represented by the table is discrete or continuous.on p. 224 Explain. If continuous, graph the functlon and find the value of ywhenfor Exs.7-9 x = 3.5. Round your answer to the nearest hundredth.

7. ;"'N~herQO)VDrent"ls,x 2

6.2

100

4

200

3 4

18.00

6 8

400300

9. 3 126 9

" AfJproJrimate weight OfWalerlpwrmsl,y 0:1 0.2 0.3 0.4,~.-~~.~.~-~--."--.---~~~~"=~-''------- -"..-....--...~-...,.""