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DYR #3 Precalc
Alg 2 Chapter 6 (old 9 ½ )
Name_______________________________
DO YOU REMEMBER??
1) Define:
a) determinant (of a matrix):
(4.3)
b) discriminant:
(5.4)
2) Write a linear system that represents the following.
Solve the system and answer the questions.
(3.3)
Puff Daddy went to the store and bought 3 CDs & 2 movies for $49.
The next week he bought 2 CDs & 4 movies for $70.
How much did each CD cost? ________ How much did each movie cost? ________
3) Sketch the graph of the system of linear inequalities.
y>0
x+ y < 5
x>1
(3.4)
4) Use a determinant to find the area of the triangle with the following vertices.
a) (-3,5) (3,-5) (2,6)
b) (0,1) (2,2) (4,3)
(4.3)
Why did you get a strange answer?
5) Find the inverse of the matrices below (if possible). Do (a) by hand & (b) with a calc.
1 1 1
1  2
a) 
b) 3 5 4
(4.4)



2

3


3 6 5
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6) Use a graphing calculator to solve the system of linear equations.
(4.5)
4x – y + z = 18
2x + 2y + 3z = 19
5x – 2y - 2z = 2
7) Find the discriminant and determine the number of real solutions.
(5.4)
4x 2  12x  9 = 0
8) Find the inverse of the function:
(6.3)
f(x) = 2x  6
9) Simplify Completely:
a)
33 5 
3
40
10) Solve for x:
2
b) 5 3
5 x4  7

1
54
=
2
2
c) 7 5 7 3
(7.4)
22
(7.5)
ANSWERS
1) det: matrix math det: dis: b2-4ac 2) $7 for a CD
$14 for a movie 3)
4b) 0, because the sides do not form a .
1 1 1
3 2


5a) 
 b) 3 2 1
2 1

3 3 2 

4a) 28

6) (2,-3,7)

7) 0, 1
8) y =
1
2
x3
3
9a) 5 5
9b)
11
12
5

16
9c) 715
10) x = 5
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11. Simplify each expression as much as possible. Remember to rationalize the
denominator if necessary.
a.
d.
5
 64x 6 y 8z 10
b.
3 x
x  5x
 2
7x x  2x 15
2
75  3 48  7 12
e.
c.
5 3
5 7
8
x 2
x 1
x2 4

12. Evaluate f (x )  3x  for the following values of x:
a. x = -2; f(x) = _____
b. x = 1.3; f(x) = _____ c. x = -2.3; f(x) = _____
13 If f(x) = x2 -2 and g(x) = x + 2, find each of the following:
a. (fg)(x)
b. (gf)(x)
c. (f-g)(x)
d. (fg)(-2)
e. (gf)(4)
f. (fg)(2)
14 Find the equation for a parabola that has vertex (-3, 5) and passes through the
point (2, -8).
_________________________
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15 Sketch the graph: y = 2x2(x-a)3(x-b)(x-c)4. Show work for end behavior, zeros,
and testing regions/multiplicity.
a
b
c
16 Write the equation for a polynomial with zeros 4, 3 - i, 3 + i
_________________________
17 Sketch the graph of the function:
y 
x2  4
x 2  6x  8
Hole: _______
Slant A: _______
Vert A: _______
x-int: _______
Horiz A: _______
y-int: _______
ANSWERS: 11a) 2xyz2 5 2xy3 11b) 7 3 11c)
5 5  15  5 7  21
11d) 1
7
2
8(x  2)
12a) -6 12b) 3 12c) -7 13a) x2+4x+2 13b) x2 13c) x2–x-4
x 1
13

13d) -2 
13e) 16 13f) 8 14) y  (x  3)2  5 16) x4-6x3-6x2
+96x-160
25
17) hole x=2; HA: y=1; VA: x=4; SA: none; x-int (-2,0) y-int (0,-½)

15)
11e)
