Algebra II

The formula for the volume of a sphere is V=3/4πr^3 What is the formula solved for r?

C

When 10b=5(c+2) is solved for c, one equation is Which of the following is an equivalent equation to find c?

…

Which graph represents the same relation as the rule y = 2x, for all real numbers x?

C

Given f(x)=10-2x find f(7).
-4
3
7
56

-4

Given b(x)=|x+4|, what is b(-10)?

6

Which table represents the same relation as the set {(-6,4),(-4,0).(-3,2).(-1,2)}

B

Given h(f)=-2(t+5)^2+4, find h(-8)
-334
-14
45
445

-14

Which graph represents the same relation as the set

{(-3,2).(5,5).(3,3).(3-2)}

Which relation below represents a one-to-one function?

D

Which graph represents the same relation as the table below?

D

What is the range of the function graphed below?

-3<y≤3

In which function is x = 2 mapped to 32?

B

The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except -3. Which of the following describes the domain of (G*f)(x)

D

If h(x) = x – 7 and g(x) = x2, which expression is equivalent to (g*h)(5)?
(5 – 7)2
(5)2 – 7
(5)2(5 – 7)
(5 – 7)x2

(5 – 7)^2

If s(x) = x – 7 and t(x) = 4×2 – x + 3, which expression is equivalent to (t*s)(x)?
4(x – 7)2 – x – 7 + 3
4(x – 7)2 – (x – 7) + 3
(4×2 – x + 3) – 7
(4×2 – x + 3)(x – 7)

4(x – 7)^2 – (x – 7) + 3

If f(x) = x2 + 1 and g(x) = x – 4, which value is equivalent to (f*g)(10)?
37
97
126
606

37

If g(x)=x+1/x-2 and h(x) = 4 – x, what is the value of (g*h)(-3)?

8/5

If m(x)=x+5/x-1 and n(x)=x-3, which function has the same domain as (m*n)(x)

h(x)=11/x-4

If g(x)=2x and (f*g)(x)=3/x, what is f(x)

f(x)=6/x

If (z*z)(x)=1/16x, what is z(x)

z(x)=x/4

If h(x) = 5 + x and k(x)=1/x, which expression is equivalent to (k*h)(x)?

1/(5+x)

If f(x)=x-3/x and g(x)=5x-4, what is the domain of (f*g)(x)?

{x|x≠4/5}

Which statement could be used to explain why the function h(x) = x3 has an inverse relation that is also a function?
The graph of h(x) passes the vertical line test.
The graph of the inverse of h(x) is a vertical line.
The graph of the inverse of h(x) passes the horizontal line test.
The graph of h(x) passes the horizontal line test.

The graph of h(x) passes the horizontal line test.

If f(x) and g(x) are inverse functions of each other, which of the following shows the graph of f(g(x))?

B.

If f(x) = 5x, what is f-1(x)?

C.

If f(x) = 3x and g(x)=1/3x which expression could be used to verify that g(x) is the inverse of f(x)?

C. 1/3(3x)

Which graph shows a function whose inverse is also a function?

A.

Which function is the inverse of f(x) = 2x + 3?

B.

Which function has an inverse that is also a function?
{(-1, -2), (0, 4), (1, 3), (5, 14), (7, 4)}
{(-1, 2), (0, 4), (1, 5), (5, 4), (7, 2)}
{(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}
{(-1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}

C. {(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}

Which statement could be used to explain why f(x) = 2x – 3 has an inverse relation that is a function?
The graph of f(x) passes the vertical line test.
f(x) is a one-to-one function.
The graph of the inverse of f(x) passes the horizontal line test.
f(x) is not a function.

B. f(x) is a one-to-one function.

If f(x) and f-1(x) are inverse functions of each other and f(x)=2x+5 what is f-1(8)?

B. 3/2

If f(x)=5x-25 and g(x)=1/5x+5

C.

The axis of symmetry of a quadratic equation is x = -3. If one of the zeroes of the equation is 4, what is the other zero?
-10
-7
-6
-4

-10

What is the vertex and the equation of the axis of symmetry of the graph of Y=x^2-6x-7?
vertex: (-16, 3)
a.o.s: x = -16
vertex: (-3, 20)
a.o.s: x = -3
vertex: (3,-16)
a.o.s: x = 3
vertex: (20, -3)
a.o.s: x = 20

vertex: (3,-16) a.o.s: x = 3

What is the equation of the axis of symmetry of the graph of y=ax^2+bx+c

x=-b/2a

What is the vertex of the graph of y = x2 + 4x?
(-2, -12)
(-2, -8)
(-2, -6)
(-2, -4)

(-2, -4)

Which function is a quadratic function?
h(t) = 12 – 8t + 6t3
g(t) = 7t2 + 3t3 + 2t
k(t) = 3t4 + 3t2 + 4
h(t) = 12 – t + 6t2

h(t) = 12 – t + 6t2

What is the axis of symmetry for the graph of y – 4x = 7 – x2 ?
x = 2
y = 2
x = 11
y = 11

x = 2

The path of a football kicked by a field goal kicker can be modeled by the equation y = -0.04×2 + 1.56x, where x is the horizontal distance in yards and y is the corresponding height in yards. What is the approximate maximum height of the football?
15.21 yd
19.5 yd
38.94 yd
45.63 yd

15.21 yd

The height of a baseball hit from a bat is modeled by a quadratic function of time, h(t). What does the second coordinate of the vertex of the quadratic function represent?
the minimum height of the baseball
the time at which the baseball hits the ground
the time at which the baseball hits the maximum height
the maximum height of the baseball

the maximum height of the baseball

The function C(x) = 400x – 0.2×2 represents the total costs for a company to produce a product, where C is the total cost in dollars and x is the number of units sold. Which statement is true?
One thousand units have the minimum cost of $200,000.
One thousand units have the maximum cost of $200,000.
Two thousand units have the minimum cost of $800,000.
Two thousand units have the maximum cost of $800,000.

One thousand units have the maximum cost of $200,000.

The cost, C, to produce b baseball bats per day is modeled by the function C(b) = 0.06b2 – 7.2b + 390. What number of bats should be produced to keep costs at a minimum?
27 bats
60 bats
174 bats
390 bats

60 bats

A rectangular patio is 9 ft by 6 ft. When the length and width are increased by the same amount, the area becomes 88 sq ft. Ginger is using the zero product property to solve the equation (6 + x)(9 + x) = 88. What do her solutions represent?
one possible length and one possible width
two possible amounts for the widths
two possible amounts for the lengths
two possible amounts by which the dimensions were increased

two possible amounts by which the dimensions were increased

The profit a company makes from producing x tabletops is modeled by the equation P(x) = 480x – 2×2. For what number of tabletops does the company make a profit of $0?
100 tabletops
120 tabletops
240 tabletops
480 tabletops

240 tabletops

The square of 9 less than a number is 3 less than the number. What is the number?
-12 or 7
-12 or -7
-7 or 12
7 or 12

7 or 12

The square of a number is 12 less than 7 times the number. What is the number?
-4 or -3
-4 or 3
-3 or 4
3 or 4

3 or 4

What are the solutions to the equation (x – 6)(x + 8) = 0?
x = -6 or x = 8
x = -6 or x = -8
x = 6 or x = -8
x = 6 or x = 8

x = 6 or x = -8

Lisa is using the equation x2 + (x – 5)2 = 157 to find two numbers that differ by 5 and that have squares that sum to 157. When Lisa solves the problem using the zero product property, what do the two solutions represent?
two numbers that differ by 5 and squares that have a sum of 157
one possible number is 5 less than the other number
one possible number that can be used to find numbers that differ by 5 and squares that have a sum of 157
two possible numbers that can be used to find numbers that differ by 5 and squares that have a sum of 157

two possible numbers that can be used to find numbers that differ by 5 and squares that have a sum of 157

What are the solutions to the equation 3(x – 4)(x + 5) = 0?
x = -4 or x = 5
x = 3, x = 4, or x = -5
x = 3, x = -4, or x = 5
x = 4 or x = -5

x = 4 or x = -5

A rectangular deck is 12 ft by 14 ft. When the length and width are increased by the same amount, the area becomes 288 sq. ft. By how much were the dimensions increased?
2 ft
4 ft
8 ft
10 ft

4 ft

The solutions to a quadratic equation are x = 2 and x = 7. If k is a nonzero constant, which of the following must be equal to the quadratic equation?

k(x-2)(x-7)=0

The solutions to the equation 2x^2+x-1=2 are x=-3/2 or

x=1

What is the solution set of the quadratic inequality 6x^2+1≤0?

slashed out 0

What are the solutions to the inequality (x-3)(x+5)≤0

{x|-5≤x≤3}

What is the solution set to the inequality (4x-3)(2x-1)≥0?

{x|x≤1/2 or x≥3/4}

An acorn falls from the branch of a tree to the ground 25 feet below. The distance, S, that the acorn is from the ground as it falls is represented by the equation S(t) = -16t2 + 25, where t is the number of seconds. For which interval of time is the acorn moving through the air?

0<t≤5/4

What is the solution set of the quadratic inequality 4(x + 2)2≤0

{x|x=-2}

What is the solution set of the quadratic inequality f(x)≥0?

{x|xER}

The graph below represents the solution set of which inequality?
-4 to 2

x2 + 2x – 8 < 0

Greg is in a car at the top of a roller-coaster ride. The distance, d, of the car from the ground as the car descends is determined by the equation d = 144 – 16t2, where t is the number of seconds it takes the car to travel down to each point on the ride. For which interval of time is Greg’s car moving in the air?

0<t<3

Reyna runs a textile company that manufactures T-shirts. The profit, p, made by the company is modeled by the function p=s2+9s-142, where s is the number of T-shirts sold. How many T-shirts should be sold to earn a profit of more than $2,000?

s > 42

If f(x) = x3 – 2×2, which expression is equivalent to f(i)?
-2 + i
-2 – i
2 + i
2 – i

2 – i

Which complex number is represented by the point graphed on the complex plane below?

3 – 4i

In which quadrant is the number -14 – 5i located on the complex plane?
I
II
III
IV

III

If f(x) = 1 – x, which value is equivalent to |f(i)|?

sqr2

if i=sqr-1 what is the value of i3

-i

If the complex number x = 3 + bi and |x|2 = 13, which is a possible value of b?

2

Which of the following is equivalent to 18-sqr-25

18-5i

Which complex number has a distance of sqr17 from the origin on the complex plane?

4 – i

What is the square root of -1?
-i
i
-1
1

i

Which complex number has an absolute value of 5?
-3 + 4i
2 + 3i
7 – 2i
9 + 4i

-3 + 4i

equation

x2 – 2x – 4 = 0

Using the quadratic formula to solve 7×2 – x = 7, what are the values of x?

B

What is the discriminant of 9×2 + 2 = 10x?
-356
-172
28
72

28

Equation

3×2 – 10x – 1 = 0

What is the discriminant of 3x^2-10x=-2?

76

If x = -3 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?

The discriminant is 0.

If the discriminant of a quadratic equation is equal to mc027-1.jpg, which statement describes the roots?
There are two complex roots.
There are two real roots.
There is one real root.
There is one complex root.

There are two complex roots.

Which equation shows the quadratic formula used correctly to solve 5×2 + 3x – 4 = 0 for x?

A

If x=6 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?

The discriminant is 0.

What is the discriminant of 3×2 + 6x = 2?
12
18
42
60

60

Which pair of equations generates graphs with the same vertex?
y = -(x + 4)2 and y = (x – 4)2
y = -4×2 and y = 4×2
y = -x2 – 4 and y = x2 + 4
y = (x – 4)2 and y = x2 + 4

y = -4×2 and y = 4×2

Which equation is y = 6×2 + 12x – 10 rewritten in vertex form?
y = 6(x + 1)2 – 11
y = 6(x + 1)2 – 10
y = 6(x + 1)2 – 4
y = 6(x + 1)2 – 16

y = 6(x + 1)2 – 16

Which phrase best describes the translation from the graph y = 6×2 to the graph of y = 6(x + 1)2?
6 unit left
6 unit right
1 unit left
1 unit right

1 unit left

Which phrase best describes the translation from the graph y = 2(x – 15)2 + 3 to the graph of y = 2(x – 11)2 + 3?
4 units to the left
4 units to the right
8 units to the left
8 units to the right

4 units to the left

Which equation has a graph that is a parabola with a vertex at (-2, 0)?
y = -2×2
y = (x + 2)2
y = (x – 2)2
y = x2 – 2

y = (x + 2)2

Which equation has a graph that is a parabola with a vertex at (5, 3)?
y = (x – 5)2 + 3
y = (x + 5)2 + 3
y = (x – 3)2 + 5
y = (x + 3)2 + 5

y = (x – 5)2 + 3

Which equation has a graph that is a parabola with a vertex at (-1, -1)?
y = (x – 1)2 + 1
y = (x – 1)2 – 1
y = (x + 1)2 + 1
y = (x + 1)2 – 1

y = (x + 1)2 – 1

What is the first step when rewriting y = -4×2 + 2x – 7 in the form y = a(x – h)2 + k?
2 must be factored from 2x – 7
-4 must be factored from -4×2 + 2x
x must be factored from -4×2 + 2x
-4 must be factored from -4×2 – 7

-4 must be factored from -4×2 + 2x

What is the first step when rewriting y = 3×2 + 9x – 18 in the form y = a(x – h)2 + k?
3 must be factored from 3×2 + 9x
x must be factored from 3×2 + 9x
9 must be factored from 9x – 18
3 must be factored from 3×2 – 18

3 must be factored from 3×2 + 9x

What is the first step when rewriting y = 6×2 + 18x + 14 in the form y = a(x – h)2 + k?
16 must be factored from 18x + 14
x must be factored from 6×2 + 18x
6 must be factored from 6×2 + 14
6 must be factored from 6×2 + 18x

6 must be factored from 6×2 + 18x

Which equation is the inverse of y = 2×2 – 8?

A

Which equation is the inverse of 2(x – 2)2 = 8(7 + y)?

D

If the domain of the square root function f(x) is mc024-1.jpg, which statement must be true?
7 is subtracted from the x-term inside the radical.
The radical is multiplied by a negative number.
7 is added to the radical term.
The x-term inside the radical has a negative coefficient.

The x-term inside the radical has a negative coefficient.

What is the domain of the square root function graphed below?

D

Which equation is the inverse of y = 100 – x2?

A

Which could be the function graphed below?

f(x)=sqr x -2

if f(x)=sqr x-3, which inequality can be used to find the domain of f(x)?

B

What is the domain of the function y=sqr x+6-7

B

Which equation can be simplified to find the inverse of y = 5×2 + 10?

A

Which equation can be simplified to find the inverse of y = 2×2?

D

Which equation is the inverse of y = 16×2 + 1?

D

Which equation can be simplified to find the inverse of y = x2 – 7?

C

Which equation is the inverse of 5y+4=(x+362+1/2

D

What is the domain of the function y=sqr x+4

C