NAME
DATE
PERIOD
Practice
Functions
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 is
the car's make and model, function
6.___1 ÿ81Yÿ41f
, //ÿ[ÿ
'
-ÿ ÿ.ÿI
7. Y
///'ÿ'
/
i '
\
/' I\1 I ÿ '8ÿ
-
8
,
oX
,
,
Nÿ
function
not a function
9. x = 5(y - 1)2
8. -x + y = 3x
oE
o
-r
x
function
not a function
Find each function value.
F"5
g
10. h(x) = x2-8x+1
11. f(a) = -3Vr-ÿ + 9
a. h(-1) 10
a. f(4) -15
b. h(2x) 4x2 - 16x + 1
b. f(3a) -9ÿ/a2 + 1
c.h(x+8) x2+8x+1
c. f(a + 1) -3ÿ/a2 + 2a + 10
5
"1-
@
State the domain of each function.
2t - 6
12. g(x) = X/-3x - 2
o
L)
{
2
}
13. h(t) - t2 + 6t + 9
{tit --/=: -3, t • R}
xlx <_ --5, x • ]ÿ
3x2 + 16ifx < -2
14. Find f(-4) and f(ll) for the piecewise function f(x) = i X/ÿ - 2 if-2 < x < 11.
L
Chapter 1
7
64; 3
-75 ifx > 11
Glencoe Precalculus
C-#-ÿI-,),-ÿ
hC,ÿ4
I 4--ÿ4-I - I0
-l-I
=- ÿÿ-I--ÿ x:+- I
. ÿ C€> -3ÿ
-- -3 J lÿ+q
,- -3 jÿ/ÿ+_,)
-5,s- ÿ-I$-
i0-,
-3 x-ÿ. >-o
-3x -ÿ a
&
,, ÿ_-ÿ
4:-g-3
t:[{; f--3, ÿ -c- ;rp.ÿ
NAME
DATE
PERIOD
Practice
Analyzing Graphs of Functions and Relations
,y
1. Use the graph of the function shown to estimate
--ÿ--12
f(-2.5), f(1), and/'(7). Then confirm the estimates
algebraically. Round to the nearest hundredth, if
N,o
z/ÿ -- 2Ix - 31 +1
/,7
-'4-ÿ-ÿ-io
1 2 3 4 5 6 7 8ÿ"
--4
--2
necessary.
12; 5; 9
/
• f
Use the graph of h to find the domain and range of each function.
•
_
R
-i!
14Y
, , ,
, , ,
[-6, 5]
=8 / io ÿ. L ix
-(
7:
---I
i i i
, , ,
4. Use the graph of the function to find its
i ,
'11111
r(x) = 4ÿ'i;-=-f - 4I
y-intercept and zeros. Then find theae values
'
algebraically, y-int: -8, zero: 2;
II
!4 -2 Io
-ÿ-- ÿ--4
2-> IIIll
Use the graph of each equation to test for symmetry with respect to
the x-axis, y-axis, and the origin. Support the answer numerically•
Then confirm algebraically.
0
,<
8
+
•
-ILL Ifly
origin;-y =-
y---ÿ41 I
-8 I--4 10
i-ÿI-T It
-
y-axis;
-x
y = -0.5(-x)2 - 3
y = --O.5(x)2 - 3
-2
zÿ.,,,..--,.ÿ,-
Z8
o_
o
\ iO:
ddd
=,
-=aÿ
I
y ÿ -ÿ0.Sx5, -31
i
C')
1
7. Graph g(x) = ÿ using a graphing calculator. Analyze the graph to
determine whether the function is even, odd, or neither. Confirm
algebraically. If odd or even, describe the symmetry of the graph of the
function.
even; f(-x) = 1 = 1= f(x); symmetric with respect to the y-axis
(-x)2
Chapter 1
xÿ
12
Glencoe Precalculus
NAME
DATE
PERIOD
Practice
Continuity, End Behavior, and Limits
Determine whether each function is continuous at the given
x-value(s). Justify using the continuity test. If discontinuous,
identify the type of discontinuity as infinite, jump, or removable.
1. f(x) -
= x-2
2 .atx=_l
2. f(x)
3x2 ,
x+4;atx=-4
x+l
3. f(x) = x3 - 2x + 2; at x = 1
4. f(x) - x2 + 3x + 2, atx= -l andx = -2
Determine between which consecutive integers the real zeros of
each function are located on the given interval.
6. g(x) = x4 + 10x - 6; [-3, 2]
5. f(x) = x3 + 5x2 - 4; [-6, 2]
[-3,-2], [0, 1]
[-5,-4], [-1, 01, [0, 1]
oo
Use the graph of each function to describe its end behavior. Support
the conjecture numerically.
@
6b
8
m
I =x2
4tV : !!
ii!
o
ÿ,
i
4m
Q.
W
i
o
-ÿ-ÿ-TÿIÿI i i i i
lim f(x)=-2; lim f(x)=-2
X-ÿ.--oo
lim f(x)=oo; lim f(X) -- oo
X-ÿ. oo
X.ÿ>--cxÿ
X.ÿ. ÿ
9. ELECTRONICS Ohm's Law gives the relationship between resistance R,
E
voltage 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.
Chapter 1
18
Glencoe Precalculus
3:
0
ccckcÿ i- 7,
04-
,=-I.
(- ÿ,-q') o lÿ, <"0
iÿ ,ÿ. 4orruxtÿa eÿ
cÿ
X.=-q
-s
J
N
<,ÿ .?Lÿ ÿ /,,ÿ-'-I- --'- "--
oo
0
-emovealotÿ o(tÿCo, hvxÿtÿ
NAME
DATE
PERIOD
Practice
Extrema and Average Rates of Change
Use the graph of each function to estimate intervals to the nearest
0.5 unit on which the function is increasing, decreasing, or constant.
Support the answer numerically.
1.
2.
, y I/".ÿ-
:
O
I
l
_
-x
increasing on (-oo, 0);
decreasing on (-oo, 0); decreasing
decreasing on (0, 1.5);
on (0, ÿ);
__
increasing on (1.5, oo);
Estimate to the nearest 0.5 unit and classify the extrema for the
graph of each function. Support the answers numerically.
3. If(x) = X4 - 3X2 + XÿJ
4.
If(x) =X3-1-x2-x
I"
|U4 r
L
tl!
.
I
=
r,I
I O-
oE
O
I
/
ÿT,,', /
!V-
)ÿ
I I
rel. min. of -8.5 at x = -1.5;
p,
[\ )
rel. max. of 1 at x = -1;
rel. min. of 0 at x = 0.5;
rel. max. of -5 at x - O;
rel. min. of -6 at x = 1;
"ÿ.
5
z,
5. GRAPHING CALCULATOR Approximate to the nearest hundredth the
relative or absolute extrema of h(x) = x5 - 6x + 1. State the x-values
where 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.
o
o
. g,(xÿ =fx ÿ+ 2xÿ/-ÿ; [-,4, ÿ21
8. PHYSICS The height t seconds after a toy rocket is launched straight up
can be modeled by the function h(t) = -1@2 + 32t + 0.5, where h(t) is in
feet. Find the maximum height of the rocket. 16.5 ft
Chapter 1
23
Glencoe Precalculus