NAME DATE PERIOD

PracticeFunctions

Write each set of numbers in set-builder and interval notation, if possible.

1. {-3, -2, -1, O, 1, ...} 2. -6.5 < x < 3

{xlx >_ -3, x e 7/,} {xI -6.5 < x < 3, x • ÿ.}; (-6.5, 3]

3. all multiples of 2 4. x < 0 or x > 8

{xlx = 2n, n • ;5} {xlx < 0 or x > 8, x • JR};(-oo, O) u (8, oo)

Determine whether each relation represents y as a function of x.

5. The input value x is a car's license plate number, and the output value y isthe car's make and model, function

6.___1 ÿ81Yÿ41f , //ÿ[ÿ 7. Y ///'ÿ'

' /

/' I\1 I ÿ '8ÿ oX x-ÿ ÿ.ÿI i ' \

,- 8 , , Nÿ

oEo-r

F-"5

g5

"1-

@

oL)

function

8. -x + y = 3x

function

Find each function value.

10. h(x) = x2-8x+1

a. h(-1) 10

b. h(2x) 4x2 - 16x + 1

c.h(x+8) x2+8x+1

not a function

9. x = 5(y - 1)2

not a function

11. f(a) = -3Vr-ÿ + 9

a. f(4) -15

b. f(3a) -9ÿ/a2 + 1

c. f(a + 1) -3ÿ/a2 + 2a + 10

State the domain of each function.

12. g(x) = X/-3x - 2

{ 2 }xlx <_ --5, x • ]ÿ

2t - 613. h(t) - t2 + 6t + 9

{tit --/=: -3, t • R}

14. Find f(-4) and f(ll) for the piecewise function f(x) = i

L

Chapter 1 7

3x2 + 16ifx < -2

X/ÿ - 2 if-2 < x < 11.

-75 ifx > 11

64; 3

Glencoe Precalculus

C-#-ÿI-,),-ÿ hC,ÿ4I 4--ÿ4-I - I0

-l-I =- ÿÿ-I--ÿ x:+- I

. ÿ C€> -3ÿ-- -3 J lÿ+q

-5,s- ÿ-I$-

,- -3 jÿ/ÿ+_,)

i0-,

-3 x-ÿ. >-o

-3x -ÿ a

,, ÿ_-ÿ&

4:-g-3

t:[{; f--3, ÿ -c- ;rp.ÿ

NAME DATE PERIOD

PracticeAnalyzing Graphs of Functions and Relations

1. Use the graph of the function shown to estimatef(-2.5), f(1), and/'(7). Then confirm the estimatesalgebraically. Round to the nearest hundredth, ifnecessary.

12; 5; 9

--ÿ--12N,o--4--2

-'4-ÿ-ÿ-io

,y

z/ÿ -- 2Ix - 31 +1/,7/

• f

1 2 3 4 5 6 7 8ÿ"

Use the graph of h to find the domain and range of each function.

_ R [-6, 5]-i!-(

, , ,• 14Y , , ,

=8 / io ÿ. L ix

7:---- i i iI , , ,

4. Use the graph of the function to find itsy-intercept and zeros. Then find theae valuesalgebraically, y-int: -8, zero: 2;

i ,

' II!4 -2 Io-ÿ-- ÿ--4

2->

'11111r(x) = 4ÿ'i;-=-f - 4I

IIIll

Use the graph of each equation to test for symmetry with respect tothe x-axis, y-axis, and the origin. Support the answer numerically•Then confirm algebraically.

• -ILL Ifly origin;-y =- -y---ÿ41 I -x-2

-8 I--4 10 zÿ.,,,..--,.ÿ,- Z8 \ iO:

=,i-ÿI-T It -=aÿI

dddy ÿ -ÿ0.Sx5, -31

y-axis;y = -0.5(-x)2 - 3y = --O.5(x)2 - 3

17. Graph g(x) = ÿ using a graphing calculator. Analyze the graph to

determine whether the function is even, odd, or neither. Confirmalgebraically. If odd or even, describe the symmetry of the graph of thefunction.

even; f(-x) = 1 = 1= f(x); symmetric with respect to the y-axis(-x)2 xÿ

0,<

8

+

o_

o

iC')

Chapter 1 12 Glencoe Precalculus

NAME DATE PERIOD

PracticeContinuity, End Behavior, and Limits

Determine whether each function is continuous at the givenx-value(s). Justify using the continuity test. If discontinuous,identify the type of discontinuity as infinite, jump, or removable.

1. f(x) - 2 .atx=_l3x2 ,

= x-22. f(x) x+4;atx=-4

3. f(x) = x3 - 2x + 2; at x = 1x+l

4. f(x) - x2 + 3x + 2, atx= -l andx = -2

Determine between which consecutive integers the real zeros ofeach function are located on the given interval.

5. f(x) = x3 + 5x2 - 4; [-6, 2]

[-5,-4], [-1, 01, [0, 1]

6. g(x) = x4 + 10x - 6; [-3, 2]

[-3,-2], [0, 1]

Use the graph of each function to describe its end behavior. Supportthe conjecture numerically.

-ÿ-ÿ-TÿIÿI i i i i

4tV : !!I =x2 i i !o ÿ,

i

lim f(x)=-2; lim f(x)=-2 lim f(x)=oo; limX-ÿ.--oo X-ÿ. oo X.ÿ>--cxÿ X.ÿ. ÿ

9. ELECTRONICS Ohm's Law gives the relationship between resistance R,Evoltage E, and current I in a circuit as R = T" If the voltage remains

constant but the current keeps increasing in the circuit, what happens to

the resistance? Resistance decreases and approaches zero.

f(X) -- oo

oo

@6b

8m

4-

mQ.W

io

3:

0

Chapter 1 18 Glencoe Precalculus

ccckcÿ i- 7,

04- ,=-I.

N

/,,ÿ-'-I- --'- "--<,ÿ .?Lÿ ÿ -

(- ÿ,-q') o lÿ, <"0

-s

iÿ ,ÿ. 4orruxtÿa eÿ cÿX.=-q

J

oo

0

-emovealotÿ o(tÿCo, hvxÿtÿ

NAME DATE PERIOD

PracticeExtrema and Average Rates of Change

Use the graph of each function to estimate intervals to the nearest0.5 unit on which the function is increasing, decreasing, or constant.Support the answer numerically.

1. 2.

, y I/".ÿ-

I lO _: -x

increasing on (-oo, 0);decreasing on (0, 1.5);increasing on (1.5, oo);

decreasing on (-oo, 0); decreasingon (0, ÿ); __

Estimate to the nearest 0.5 unit and classify the extrema for thegraph of each function. Support the answers numerically.

oEOI

p,"ÿ.5

z,

@

oo

3. If(x) = X4 - 3X2 + XÿJ 4.

|U4 rL tl! . r,I

/ ÿT,,', / I I

!V-rel. min. of -8.5 at x = -1.5;rel. max. of -5 at x - O;rel. min. of -6 at x = 1;

If(x) =X3-1-x2-x

I"

I= [\ )

I O- )ÿ

rel. max. of 1 at x = -1;rel. min. of 0 at x = 0.5;

5. GRAPHING CALCULATOR Approximate to the nearest hundredth therelative or absolute extrema of h(x) = x5 - 6x + 1. State the x-valueswhere they occur.

rel. max. (-1.05, 6.02); rel. min. (1.05, -4.02)

inld' the averagÿNrate of change of each £unct/ion on the ÿivenÿinteÿval.

. g,(xÿ =fx ÿ+ 2xÿ/-ÿ; [-,4, ÿ21

8. PHYSICS The height t seconds after a toy rocket is launched straight upcan be modeled by the function h(t) = -1@2 + 32t + 0.5, where h(t) is infeet. Find the maximum height of the rocket. 16.5 ft

Chapter 1 23 Glencoe Precalculus