Algebra 2
Name
/ÿ
CHAPTER 1 REVIEW
1. Micah was given $200 for his birthday. Each week he spends $15 on comic books. In
how many weeks will his birthday money be gone?
Create multiple representations (x --> y table, graph and equation) for the relationship
between the weeks since Micah's birthday and how much money he has left. How does
each representation show the solution to the problem?
TABLE:
EQUATION:
/: ÿlO0 -!ÿx
GRAPH:
I
I
too
\
go
\
IUo
o
\
"\
N.
Wo
3ÿo
,t
ÿ.-
ÿ
V
ÿ
b
") f.
ÿ,
€0
¢4
i.a-
2. Graph each equation :and find the x- and y-intercepts'
a.
y=--3x+8
2
ÿ-/ÿ,
(/¢ÿo)
ÿ/-/,ÿ t
(0/{)
b.
y-i,ÿ 7-,
2x - 3y = -6
V
7
\ i
ii
f
f
-! k= -i'J<
Z:
/
f
h"ÿ,,
/!
/'1
Jf
)c
\
3. Graph the function f(x) = x2 - x - 6. Identify the domain and range, any special
points and describe any symmetry, fÿ.ÿ)(Xfÿ)Z=cy
Range:
- {ÿ. D-ÿ; ÿ ÿ/ /- ÿ ÿ L'- (ÿ.D<-s l ÿ)
Special Points:
/
/
\
\
/
\ /
(ÿ,o) (-ÿ,oÿ
(x-intercepts)
3"
(0,-6)
/I
(y-intercept)
(max. or rain.)
Symmeÿy:
L, ÿ)a. _(, ÿ) _
- L,, ÿ--;
<
4. Given the functions f(x) = xÿ and g(x) = x2 - x, fmd each of the following.
a. f(s)
b. g(-1)
,!'g;V
? {-,,j -,{-i)ÿ-{-!)
'= ! -}J
c. xiff(x)=10
L
d.
x if g(x) = 6
"z.-
I0 = x0"77-ÿ
100:-Xiq
(ÿ:-3) Lx rÿJ "- o
5. Find the x- and y- intercepts for
a. y=x2-3x-18
{/,)<-'; ÿ/yÿ. )
x-intercepts:
( @ 0) d-3, o)
y-intercept:
(o,-ie)
b. 5x-7y=35
x-intercept:
s
=?
(7,0)
y-intercept: -)
7 :s (O)ÿ'-71d)-72
6. Describe the domain and range for each fimction shown below.
a.
f£{: ...... I ......... r-T=
b,
-t--ÿ
• I
y
: r3: ::r:) ÿr;ÿ J
........ } -3 -ÿ -
L.L
Domain: - <,a ,ÿ J< < ÿ, ÿ (-mj 6,)
Domain:
Range: - ÿo ÿxi ÿ_ 6, oÿ (-ÿ]ÿ.ÿ
Range:
--- <,o ÿ x ÿ ÿ ÿ (- ÿL, 0o)
-{± ÿj-ÿ ÿ
ÿ
ÿ'-ÿ,ÿ
7. Use the Pythagorean Theorem to find the value ofx.
15
X=9
12
X
8. Solve for y.
a.
b.
9. Rewrite each equation as an equivalent equation without fractions and then solve.
a,
x+2_10-2x
5
3
b.ÿ 3_1=8)X
x
"3" 9x
18x . qc/
/3
5
J
5
_ÿ
10. Determine where the graphs of these equations intersect using your calculator.
a.
y=3x+15
b.
y=3-3x
y=x2-3x-8
y=2
O -ÿ (/" { )( x/a-5
y ÿ % ("ÿ) I i2"
y: {@ÿ-{{{)-,
y ÿ (,,.a.} ">--.T(..ÿj.. o
'¢;f,
11. Find an equation for each of the lines described below
a. The line that passes through the point (2,8) and has a slope of-5.
y=- -d<, J2"
b :-- t d"
b. The line that passes through the points (-3,4) and (5,-4).
y h -X ÿ/
C.
The line that passes through the points (-2,4) and (4,-5).
c4 -ÿ ÿ(-z)/b
z-
ÿ .....
°
?
12. What is the equation for the graph.
13. Solve
3x-4y =12
y=5x-3
b.
8..
y=2x+6
×=-3
7x+4y=8
Y =/5-ÿ
-V7 =ÿ;
y =/ÿ-
x+y=6
d. 51 =5x-4
C.
y = 2x
{3 ÿ- Sx
Xÿ- (ÿ×) =(,
x=//
X >gÿ
e,
2x - 5(x + 4) = -2(x + 3)
f.
(x - 3)(2x + 7) = 0
X=¢
ÿ_Xÿ)=o
;ÿX > -2
y= //
y =-/q
2.