Algebra 2B Mid-Term Review Problems
Name:
1. Which of these does NOT have the ,same value as the others?
A. log28
(B. log 9
D. 1og5125
C. log464
2. Which function represents exponential growth?
A. y = 2.5x13
c C. y = 2.5 (1.3)X
B. y = -2.5x13
D. y = 2.5 (0.3)x
Sketch each graph. Label 3 points and the asymptote. Also name the domain & range.
3.
f (x) log3 x
domain: (0) r.›.0
otc>
range:
4. g(x) =- - -1
3
domain:
0 y
range:
/1
4
ti
4
•
6. g(x) = log3 (x - 3) + 2
5. h(x) = - .2x+1
2
(_
domain: /72-,
domain:
range:
A
••••
4
3/
(/
V
7. Describe the vertical asymptotes and holes for the graph of the rational-function.
1
1
2
'
4-, K -7
x +4x+3
(XL-3Y/it 1)
8. Simplify
a+b a2 +b2
3
12
\
X
v-
x+5
9. Determine the coordinates for any holes in the graph of f(x)= 2
x +6x+5
—
4x
+1
3x2
10. Sketch the graph of the rational function y = 2
x + x -6
-7)
(-3
A
()(
1
V7 3
p.
•
J
J
AI/
4
V
•
11. Sketch the asymptotes and the graph of the equation.
Y=
x+1
(x-
12. Find any points of discontinuity for the rational function.
(x —1)(x —2)(x +3)
Y=
(x +1)(x — 2)
—
1114,
Simplify and state any restrictions
7
2x2 + 5x + 2 2x2 + x —
13.
4x2 -1
x' + x —
X
I
14.
3
1
8x3y3 4xy
,X4
2
x+3
15.
1
2
x +3
7+
16.
5x
4
x2 +4x+4
-
7 f)(
)(it -2-) a(A z)
Solve each equation.
17.
4 =
5
2
x-1 x -2x+1
18. 11 1=-—4 Ei
3x 3 x'
19.
4
+
x-1
20.
11 1 4
—+=
3x 3 x'
22.
30
3
+
m2 -25 m-5
24.
375 + 24y3
21.
5
— 2x +1
--
0(
,y)(--1)
3x
4
x2 -7x-18 x2 +10x+16
Factor Completely
23.
27x3 —64 `(
3
25. An angle drawn in standard position has a terminal side that passes through the point
I / /7the measure of the angle [0,270?
6
. What is
26. An angle of 225° is in standard,position. What ,aretle coordinates of the point at which the terminal side
intersects the unit circ ?
)
( -5_ )
27.
28.
What is the exact value of sin
3
Describe the translations from the parent function y = cos 01 to the new function: y =3 cos (40 — 2)+5
/4---,/ pp /not ;
Pt-712-/ obi Tr
Graph One Period:
29. y = -2sin 'r x
30. y = tan 2x
31. y = cos gx