Download College Algebra Math 1314 Review Find the center

College Algebra
Math 1314
Review
Find the center-radius form of the equation of the circle.
1) center (-6, -4), radius 3
A) (x + 4)2 + (y + 6)2 = 3
B) (x + 6)2 + (y + 4)2 = 9
D) (x - 4)2 + (y - 6)2 = 3
C) (x - 6)2 + (y - 4)2 = 9
Find the center and radius of the circle.
2) x2 + y2 + 8x - 10y - 8 = 0
A) center: (5, -4); radius: 7
C) center: (4, -5); radius: 49
B) center: (-4, 5); radius: 7
D) center: (-5, 4); radius: 49
Decide whether the relation defines a function.
3)
A) Function
B) Not a function
The graph of y = f(x) is given. Use the graph to find the function value.
4) Find f(16).
20
20
-20
-20
A) 28
B) 8
C) 16
1
D) 20
Give the domain and range of the relation.
5)
A) domain: (- , 3]; range: [0, 3]
C) domain: [0, 3]; range: (- , 3]
B) domain: [-1, 3]; range: [-3, 0]
D) domain: [-3, 0]; range: [-1, 3]
6) y = x2 + 4
A) domain: (- , ); range: [4, )
C) domain: (-4, ); range: (- , )
7) y =
6x - 4
A) domain: (
C) domain:
8) y =
, ); range:
2
,
3
; range: (
B) domain: (- , ); range: (-4, )
D) domain: (4, ); range: (- , )
2
,
3
, )
B) domain:
2
,
3
; range: [0, )
D) domain:
2
,
3
; range: [0, )
6
9-x
A) domain: (- , 9) (9, ); range: (- , )
C) domain: (- , ); range: (- , 0) (0, )
B) domain: (- , 9) (9, ); range: (- , 0)
D) domain: (- , ); range: (- , )
Find the requested value.
7x + 7, if x 0
9) f(4) for f(x) = 2 - 3x, if 0 < x < 3
x,
if x 3
A) 35
B) 4
C) -10
2
D) 3
(0, )
x 2 - 9, if x < -1
10) Graph the function: f(x) = 0,
if -1 x 1
x 2 + 9, if x > 1
A)
B)
C)
D)
Compute and simplify the difference quotient
f(x + h) - f(x)
,h
h
0.
11) f(x) = 8x - 15
A) -15h
12) f(x) = 3x 2 + 5x
A) 6x 2 + 3h + 5x
13) f(x) =
15
8
B) 15
C)
B) 9x - 5h + 10
C) 6x + 3h + 5
15
x + 20
A) C) -
15
B)
(x + 15)2
300
(x + h + 20)(x + 20)
15
(x + h + 20)(x + 20)
D) -
3
15
(x + h + 20)(x + 20)
D) 8
D) 6x + 5
14) Graph the function: y = |x - 7| + 2
A)
B)
C)
D)
4
15) Graph the function: g(x) = -
x+1+1
A)
B)
C)
D)
16) Select the equation that describes the graph shown.
A) y = (x + 5)2 + 2
Identify the vertex of the parabola.
17) y = -2x 2 + 8x - 8
A) (0, 2)
B) y = (x - 5)2 + 2
C) y = (x + 2) 2 - 5
D) y = x 2 - 5
B) (0, -2)
C) (-2, 0)
D) (2, 0)
5
18) The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches:
M(x) = 19x - x2 . What rainfall produces the maximum number of mosquitoes?
A) 361 in.
B) 0 in.
C) 9.5 in.
D) 19 in.
19) Your company uses the quadratic model y = -11x 2 + 350x to represent how many units (y) of a new product
will be sold (x) weeks after its release . How many units can you expect to sell in week 20?
A) 6780 units
B) 2600 units
C) 7220 units
D) 11,400 units
For the pair of functions, find the indicated sum, difference, product, or quotient.
20) f(x) = 9x - 4, g(x) = 7x - 9
Find (f - g)(x).
A) 16x - 13
B) -2x - 5
C) 2x - 13
D) 2x + 5
For the given functions f and g , find the indicated composition.
21) f(x) = 4x 2 + 3x + 7, g(x) = 3x - 5
(g f)(x)
A) 4x2 + 9x + 16
B) 12x 2 + 9x + 16
C) 4x2 + 3x + 2
D) 12x 2 + 9x + 26
Use synthetic division to perform the division.
x 3 - x2 + 4
22)
x+2
A) x2 - 3x + 6 +
-8
x+2
B) x2 - 3x + 6 +
6
x+2
C) x2 - 2x + 6 +
6
x+2
D) x2 + 3x + 6 +
-8
x+2
Factor f(x) into linear factors given that k is a zero of f(x).
23) f(x) = x 3 - 3x 2 - 25x + 75 ; k = 5
A) (x - 5)(x - 3)(x + 3)
B) (x - 5)(x + 3)(x + 5)
C) x(x - 5)(x - 3)
D) (x - 5)(x - 3)(x + 5)
C) 1 + 2i, 1 - 2i
D) 1 +
For the polynomial, one zero is given. Find all others.
24) P(x) = x3 - 3x2 + 7x - 5; 1
A) 1 +
5, 1 -
5
B) -1 + 2i, -1 - 2i
Give all possible rational zeros for the following polynomial.
25) P(x) = 2x3 + 8x 2 + 5x - 8
A) ±1, ±1/2, ±1/4, ±1/8, ±2
C) ±1, ±2, ±4, ±8
Find all rational zeros and factor f(x).
26) f(x) = x 3 + 6x 2 - 9x - 54
A) 3, 6, -3; f(x) = (x - 3)(x - 6)(x + 3)
C) -4, -6, 6; f(x) = (x + 4)(x + 6)(x - 6)
5i, 1 -
B) ±1, ±2, ±4
D) ±1, ±1/2, ±2, ±4, ±8
B) -3, -6, 3; f(x) = (x + 3)(x + 6)(x - 3)
D) 4, 6, -6; f(x) = (x - 4)(x - 6)(x + 6)
6
5i
27) The graph of f(x) = x3 - x 2 - 8x + 12 is shown below. Use the graph to factor f(x).
A) f(x) = -(x + 3)(x - 2)2
C) f(x) = (x + 3)(x - 2) 2
B) f(x) = x(x + 3)(x - 2)
D) f(x) = (x - 3)(x + 2) 2
Find the correct end behavior diagram for the given polynomial function.
28) P(x) = -x 5 - 7x 3 - 4x + 1
A)
B)
C)
Graph the polynomial function. Factor first if the expression is not in factored form.
29) f(x) = (-2x - 2)(x + 1)(x - 1)
A)
B)
C)
D)
7
D)
Find any vertical asymptotes.
x-6
30) f(x) =
x 2 + 3x
A) x = 0, x = -3
B) x = 3
C) x = -3
D) x = 6
C) None
D) y = 1
C) y = 2
D) None
Find the horizontal asymptote of the given function.
x+ 9
31) g(x) =
x2 - 6
A) y = 0
32) h(x) =
B) y = 6
16x 2
8x 2 - 3
A) y = 3
B) y =
3
Determine whether or not the function is one-to-one.
33)
A) No
B) Yes
If f is one-to-one, find an equation for its inverse.
34) f(x) = -5x + 1
1
1
1
A) f-1 (x) = - x +
B) f-1 (x) = - x - 1
5
5
5
1
C) f-1 (x) = - x + 1
5
1
1
D) f-1 (x) = - x 5
5
35) f(x) = x 3 - 1
B) f-1 (x) =
A) Not a one-to-one function
3
C) f-1 (x) = x + 1
D) f-1 (x) =
Solve the equation. If necessary, round to the nearest thousandth.
36) 2(x - 1) = 17
A) {9.500}
37) 8e7x+5 = 9
A) {-1.857}
3
3
x-1
x+1
B) {5.087}
C) {3.087}
D) {3.140}
B) {-0.697}
C) {0.463}
D) {-1.891}
8
Write the expression as a sum, difference, or product of logarithms. Assume that all variables represent positive real
numbers.
38) log b
A)
4x 9
z2
log b4 +
C) log b2 + +
logbx 9 9
log bx
2
9
B) log b2 + logbx - 1log bz
2
logbz 2
÷ 1log bz
D) log b2 ·
9
logbx - 1logbz
2
Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that
all variables represent positive real numbers.
39) 3 log 4 (2x + 4) + 4 log 4 (5x + 5)
A) log 4
(2x + 4)3
B) log 4 (2x + 4)3 (5x + 5)4
(5x + 5)4
C) log 4 ((2x + 4)3 + (5x + 5)4 )
D) 12 log 4 (2x + 4)(5x + 5)
Solve the equation and express the solution in exact form.
40) log (x + 3) = 1 - log x
A) -5, 2
B) 2
C) -2
D) -2, 5
Solve the problem.
41) Find the number of years for $4800 to grow to $9400 at 6% compounded quarterly. Round to the nearest tenth
of a year.
A) 11.1 years
B) 10.4 years
C) 13.5 years
D) 11.3 years
Use a matrix method to solve the system of equations. If the system has infinitely many solutions, let the last variable
be the arbitrary variable.
42) 6x + 9y - z = 101
x - 9y - 2z = -64
9x + y + z = 74
A) {(7, 4, 7)}
B) {(7, 7, 4)}
C) {(-7, 7, 14)}
D)
Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
43) x2 - y2 = 39
x - y = 3
A) {(-8, -5)}
B) {(8, -5)}
Find the indicated matrix.
1
-1
44) Let C = -3 and D = 3 . Find C - 4D.
2
2
A)
B)
5
-3
9
-15
-6
-6
9
C) {(8, 5)}
D) {(-8, 5)}
C)
D)
5
-6
4
-5
15
6
45) Given A =
A)
C)
5 -1
-3 2
and B = 0 -1 , find AB and BA.
4 -3
B)
0 1 ; BA =
0 1
AB =
-12 -6
-12 -6
AB =
D)
AB = 3 -2 ; BA = -4 -2
29 -10
8 -3
10
4 -8 ; BA = -3 2
-8 9
11 2
AB = -4 -2 ; BA = 3 -2
8 -3
29 -10