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Rev 1-15-16

Name ~~~~~~~~~~~~-

Date ~~~~~~~~~~~~~

Tl-84+ GC 21 Graphing Piecewise Functions

Objectives: Use TEST to compare a single value of a variable to a test value Use TEST to compare many values of a variable to a test value Multiply a function by a TEST result to limit domain and graph a piece Determine if your GC will show y = 0 when multiplied, use divide by a TEST result Add pieces to graph a piecewise function

The TEST menu is the second function above MA TH: .... ~

LOGIC

3:) 4·> ·-5:( 6=~

We can select from the list by typing the corresponding number. "Less than" is option 5, for example.

Example 1: Use GC to determine if a) 6<10 b) 6~3

a) Use the TEST menu to determine if 6 < 10

The GC says 1 ifthe answer to the question is true (or yes). 6 < 10 is a true statement, so GC says 1.

b) Use the TEST menu to determine if 6;;:::: 3

The GC says 0 if the answer to the question is false (or no). 3 is a false statement, so GC says 0.

653

I

6<10

I

0

1

yright 2016 by Martha Fidler Carey. Pennission to reproduce is given only to current Southwestern College instructors and students.

~

Rev 1-15-16

TI-84+ GC 21 Graphing Piecewise Functions page 2

~Example 2: Use GC to store x = -1 in memory and determine if a) x < 10 b) x~3

Store x = -1 in memory location x (graphing x).

a) Test x < 10

...... ~Li] (CATo~) [:] The GC tests the value stored in memory, and concludes that yes, -1<10.

b) Test x ~ 3 -1-+x

X<10

X~3

-1

-1-+X

X<10

I

L-~~~~~~~--'

-1

1

0 ...... ~~~. '--~~~~~~~---'

The GC tests the value stored in memory, and concludes that no, -1~3is a false statement.

Example 3: Graph the TEST results for a) x :S 4 b) x >-2

CAUTION: We are NOT graphing the inequality x :S 4, which would be graphed on a number line.

TEST gives y-coordinate that is 0 or 1, depending on whether x is less than or equal to 4 (y-coordinate 1) or not less than or equal to 4 (y-coordinate 0).

The GC automatically generates the values of x from Xmin and Xmax in WINDOW.

,~ (SWROrfl] a) Type the test x :S 4 as a function in the Y= menu, then graph in a standard viewing window.

Copyright 2016 by Martha Fidler Carey. Pennlsslon to reproduce Is given only to current Southwestern College instructors and students.

Rev 1-15-16

TI-84+ GC 21 Graphing Piecewise Functions page 3

~Example 3, continued

c c ' ' '

' c

f'lot1 Plot2: -...Y1 EIX541 -...Yi.= -...YJ:= -...Y1t= -...Ys:= ,y,= -...Y7=

PlotJ:

The GC graphs a horizontal line y = 1 for all x values up to x = 4 , then a horizontal line y = 0 for all x-values

after 4. It's hard to tell h t · d"d t ti 4 without checking a table. wait 1 a exac ty x = x Y1

0 1 1 1 2: 1 J: 1

" 1 !> 0 I~ 0

X=6 x = 4 has y-value 1.

~ b) Type the test x > -2as a function in the Y= menu, then graph in a standard viewing window.

{':.,,]~ '--~~~~~~~~~

f'lot1 Plot2: f'lotJ: -...Y1 EIX>-21 -...Y2:= '-YJ:= '-Y1t= -...Ys:= ,y,= ,y.,=

The GC graphs a horizontal line y = 0 for all x values before x = -2, then a horizontal line y = 1 for all x-x Y1

a 0 -1 1 0 1 1 1 2: 1 3: 1 If 1

values after -2. X=-2 The table shows that x = -2 is assignedy-coordinate 0.

Copyright 2016 by Martha Fidler Carey. Pennisslon to reproduce ls given only to current Southwestern College instructors and students.

Rev 1-15-16

TI-84+ GC 21 Graphing Piecewise Functions page 4

~Example 4: Graph the function f(x) = 2x+ 3 for the domain x ~Oby multiplying by the TEST results

for its domain.

I CAUTION: We want the function value times the test value, so we need to include additional parentheses!

~ L!::_J

Pltt1 Pltt2 Pltt3 -...V1E1<2X+3)*(X50) -...V2=I -...V3= .... v .. = -...vs:= 'Vii= -...v1=

CAUTION: If you have a new color calculator, you may see a horizontal line y = 0 for the x-values on the right side of the graph. You can remove this by DIVIDING by the test value. Newer calculators do not graph values that result in + 0 .

...... ~~ . . ~ ~

CAUTION: However, if you have an older calculator, dividing by the test value will completely confuse your calculator and it may graph nothing at all!

{2x+3 x~ 0

Example 5: Graph the piecewise function f(x) = by multiplying each piece by TEST -x-1 x>O

results for its domain using two lines of the y= menu.

~The first piece is the same as Example 4. We continue with the second piece in y 2 :

Copyright 2016 by Martha Fidler Carey. Pennlssion to reproduce is given only to current Southwestern College Instructors and students.

Rev 1-15-16

TI-84+ GC 21 Graphing Piecewise Functions page 5

·~ Example 5, continued

~f091 ~L:!_J

~ .. (JWJ~ ~ ; L::._J L_!_J

...... ~L!J Plot1 Plot2 PlotJ:

-...Y1 El<2X+3)/(X::;0) -...Y2:EI( -X-1 )*(X)0) -...YJ:=I ,y .. = -...Ys= -...Yli= -...y7:

CAUTION: When you transfer this graph to paper, you must clearly indicate which piece includes its endpoint (closed circle) and which piece does not (open circle)!

REMEMBER: A piecewise function is still a single function, and the resulting graph must pass the vertical line test!

{3 x < -1

~Example 6: Graph the piecewise function /(x) = 2 -x +4 x~-1

We expect the first piece to be a horizontal line while the second piece is a parabola.

Plot1 Plot2: PlotJ: ,y1 El3*<X< -1) -...Y2E1( -X2+4)*<X~ ·~ -...YJ:=I ,y .. = -...Ys= -...Y&=

~~ ~L_!_J

Copyright 2016 by Martha Fidler Carey. Pennission to reproduce Is given only to current Southwestern College instructors and students.

.·

Rev l-15-16

TI-84+ GC 21 Graphing Piecewise Functions page 6

Practice: Graph the piecewise function.

{x+2 x<l

1) Graph f(x) = 2x+l x ~I

{-2x+4 x ::5:-1

2) Graph f(x) = 3 x>-l

{x-l x'.5:3

3) Graph f(x) = -x+5 x>3

4) Graph f(x) = {4x-4 x < 2 -x+l x;:::2

{-3x x ::5:-2

5) Graph f(x) = 3x+2 x >-2

{-1 x<-3

6) Graph f(x) = 2 x~-3

{-x+7 x <-l

7) Graph f(x) = 2 ~ -x +9 x;:::-1

Copyright 2016 by Martha Fidler Carey. Permission to reproduce Is given only to current Southwestern College Instructors and students.

Rev 1-15-16

TI-84+ GC 21 Graphing Piecewise Functions Solutions, page 7

tloti t1ot2: t1ot3 -...Y1El<X+2>*<X<1) -...Y2:El(2X+1 )*(X;::t) ,y3: 'Y"= -...Ys:= -...Ylli= -..,y7: 1) ,___ _______ ___,..___ _______ ___.

2)

4)

5)

6)

7)

t1ot1 t1ot2: t1ot3 -...Y1 El( -2X+4)*<X~ • -...Y2:El3*<X>-1) -...Y3=I ,y .. = -...Ys:= 'Ylli= ,y7:

tloti t1ot2: t1ot3 -...Y1E1<4X-4>*<X<2> -...Y2:EI( -X+1 >*<X;::2) -...Y3=I ,y .. = -...Ys:= -...Ylli= ,y7:

tloti t1ot2: tlotl -...Y1 El( -3X)*(X~ -2) -...Y2:El(3X+2>*<X> -:• -...Y3=I 'Y"= -...Ys:= -...Ylli= ,y7:

tlot1 t1ot2: tlotl -...Y1 El< -1 )*<X< -3) -...Y211<2)*(X;::-3) -...Y3=I ,y .. = -...Ys:= -...Ylli= ,y7:

tloti tlot2 tlot3 -...Y1 El( -X+7)*<X< - • .... Yi a ( -x2:+9) * < x;:: ·• -...Y3= .... v .. = -...Ys:= -...Ylli=

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Copyright 2016 by Martha Fldle~ Carey. Pennission to reproduce Is given only to current Southwestern College instructors and students.