Alg Cumulative Review Semester test
8x⁵
(-2x³)(-4x²)
4x⁶
(-2x³)²
-27x⁶
(-3x²)³
8x³y³
(2xy)³
12x⁶
(3x)(4x⁵)
27x⁹
(3x³)³
u≤-12
(u/4)≤ -3
x⁵
(x²)(x³)
x⁷
(x⁴)(x³)
3x(-4x)
-12x²
24≥w or w≤24
-15 ≤ 3 - ¾ w
1 < x < 3
-2 < -3x + 7 < 4
-6 < x < 1
-20 < 3x - 2 < 1
(-3x²)³
-27x⁶
x < 2 or x > 3
-2x + 7 > 3 or 3x - 4 > 5
-1 < x < 4
-3 < 2x - 1 < 7
1 < x < 4
-4 < x - 5 < - 1
-4(n+1)
-4n-4
(6,-6)
-4x - 2y = -12 4x + 8y = -24
(1,-4)
-4x - 6y = 20 -4x + 5y = -24
8x⁶
-4x³(-2x³)
-5 < x < 7
-6 < x - 1 < 6
Solve 82 ≥ 10 - 9x > -71
-8 ≤ x < 9
2.5 < x < 4
-9 < -2x - 1 < -6
p≤1
-p - 2 ≤ 9(2 - 3p) + 6
(23x^9) ^0
1
3 < x < 4
1 + x < 5 < 2 + x
( 81 x^12) ^ (-3/4)
1/(27 x^9)
100 ^ (-1/2)
1/10
27 ^ (-1/3)
1/3
16 ^ (-3/4)
1/8
x⁻⁴
1/x⁴
6n(2n + 3)
12n^2 + 18n
(2n+2)(6n+1)
12n^2+14n+2
(3x)(4x⁵)
12x⁶
64 ^ (2/3)
16
(2r-3)(9r-6)
18r^2-39r+18
-2 < x < -1
2 + 3x < -1 < 3x + 5
Solve 3 ≤ - 7 + 5x < 33
2 ≤ x < 8
no solution
2(6u - 1) - 3u > 9u + 8
a = -6 b = 2 y-intercept (0, -6)
2. Name the a, b, y-intercept of f(x) = -6(2)^x
(3x³)³
27x⁹
2 < x < 3
2x - 3 < x and 2x + 1 > x + 3
(4,3)
2x - 3y = -1 y = x - 1
(4 x^10) ^(1/2)
2x^5
x < -7 or x > 4
3 - 2x > 17 or 5x - 3 > 17
-1/3 < x < 5/6
3 < 5 + 6x < 10
3x⁻³
3/x³
(4 x^4 )^ (5/2)
32 x^(10)
10 < c < 12
37 < 3x + 7 < 43
x<-1
3x - 5 < -8
x > 4 or x < 2
3x - 7 > x + 1 or 4x - 5 < 3x - 3
-12x²
3x(-4x)
3/x³
3x⁻³
16 ^ (1/2)
4
(d-5)(4d-8)
4d^2-28d+40
x < - 2 or x > 3
4x + 3 < -5 or -2x + 7 < 1
x<10
4x - 3 < 2x + 17
(2x+4)(2x-4)
4x^2 - 16
(8 x^9 ) ^(2/3)
4x^6
(-2x³)²
4x⁶
(25 x^16) ^ (1/2)
5 x^8
(-6,0)
5x + 4y = -30 3x - 9y = -18
x < 4 or x > 8.4
6x - 15 > 9 or 10x > 84
x > 2 or x < 3
7 - 3x > 1 or 5x + 2 > 17
-4 < x < -2
7 < -3x + 1 < 13
4 ^ (3/2)
8
5 < x < 7
8 < x + 3 < 10
(4n+1)(2n+1)
8n^2+26n+6
(-1,-8)
8x + y = -16 -3x + y = -5
(2xy)³
8x³y³
(-2x³)(-4x²)
8x⁵
-4x³(-2x³)
8x⁶
p≤8/11
9 +8p ≤ 17 - 3p
x > 5
9x - 5x > 20 and 8x > - 36
y = 199x + 999
A car is listed for sale with monthly payments of $199, and a downpayment of $999. Write the money paid for the car as a function of the number of monthly payments.
y = 239x + 1200
A car is listed for sale with monthly payments of $239, and a downpayment of $1200. Write the money paid for the car as a function of the number of monthly payments.
y= 309x + 3200
A car is listed for sale with monthly payments of $309, and a downpayment of $3200. Write the money paid for the car as a function of the number of monthly payments.
y= 200x + 20
A concert is $200 per ticket and the cost of parking is $20. Write the equation that models the total cost of the attending the concert, as a function of the number of tickets purchased.
y = 25x + 40
A concert is $25 per ticket and the cost of parking is $40. Write the equation that models the total cost of the attending the concert, as a function of the number of tickets purchased.
y = 250x
A concert is $250 per ticket and the cost of parking is free. Write the equation that models the total cost of the attending the concert, as a function of the number of tickets purchased.
f(x) = 0.5x + 12
A large 3 topping pizza costs $12. Each additional topping costs 50c. Write the cost of the pizza as a function of the number of additional toppings.
f(x) = 0.5(x - 3) + 12
A large 3 topping pizza costs $12. Each additional topping costs 50c. Write the cost of the pizza as a function of the number of toppings.
f(x) = 0.5x + 10
A large pizza costs $10. Each topping costs 50c. Write the cost of the pizza as a function of the number of toppings.
f(x) = 0.75x + 12.5
A large pizza costs $12.50. Each topping costs 75c. Write the cost of the pizza as a function of the number of toppings.
Polynomial
A monomial or the sum of monomials
Polynomial in standard form
A polynomial arranged in order of greatest degree monomial term to smallest from left to right
Monomial
A polynomial with just one term (mono- means one)
The drug
A scientist studies the impact of a drug on cancer. What is the independent variable?
L = A/W
Area of a rectangle A = LW Solve for L
y= 1.5x + 10.95
At a waterpark, souvenir mugs cost $10.95. Refills of soda cost $1.50 each. Write the cost of soda for the day as a function of number of refills.
y= 2x + 9.95
At a waterpark, souvenir mugs cost $9.95. Refills of soda cost $2 each. Write the cost of soda for the day as a function of number of refills.
y = 1.25x + 12.95
At the waterpark, souvenir mugs cost $12.95. Refills of soda cost $1.25 each. Write the cost of soda for the day as a function of number of refills.
y= -10x + 100
Bill is repaying a $100 loan at $10 per week. Write the equation that models the amount left to pay back to the weeks.
y = 10x + 10
Bowling costs $10 per game and $10 for shoe rental. Create a function that represents the costs of bowling as a function of the number of games played.
y = 8x + 12
Bowling costs $12 for shoe rental and $8 per game . Create a function that represents the costs of bowling as a function of the number of games played.
y = 7.5x + 10
Bowling costs $7.50 per game, plus $10 for shoe rental. Create a function that represents the costs of bowling as a function of the number of games played.
197
C(-10) = ?
47
C(-5) = ?
all real numbers
Describe the domain of the function f(x) = -(4)^x
As x--> positive infinity, y --> 0. As x--> negative infinity, y -->negative infinity.
Describe the end behavior f(x) = -3(0.8)^x
As x--> positive infinity, y --> 0. As x--> negative infinity, y -->positive infinity.
Describe the end behavior f(x) = 3(0.8)^x
As x--> positive infinity, y --> negative infinity. As x--> negative infinity, y --> 0.
Describe the end behavior for the exponential function f(x) = -2(6)^x
As x--> positive infinity, y --> positive infinity. As x--> negative infinity, y --> 0.
Describe the end behavior for the exponential function f(x) = 2(3)^x
y<0
Describe the range of the function f(x) = -2(3)^x
y>0
Describe the range of the function f(x) = 2(3)^x
(2a - 5)(2a + 5)
Factor Completely
(3a + 7)(2a + 3)
Factor Completely
(3v + 2)(v - 1)
Factor Completely
(3x - 1)(x + 3)
Factor Completely
(4k + 1)(4k - 1)
Factor Completely
(n - 7)(10n + 1)
Factor Completely
(r + 6)(r - 9)
Factor Completely
(x - 9)(x - 4)
Factor Completely
6(x - 1)(9x - 8)
Factor Completely
2
Find f(-10)
3
Find f(-4)
-1
Find f(0)
-3
Find f(1)
-4
Find f(4)
(-0.25, 1.5)
Find the solution.
(-2, -2)
Find the solution.
(0, 0)
Find the solution.
(0, 3)
Find the solution.
(2, 20)
Find the solution.
(2, 3)
Find the solution.
(2, 4)
Find the solution.
(2, 6)
Find the solution.
(2, 8)
Find the solution.
(2/3, 20/3)
Find the solution.
(3, 2)
Find the solution.
(3, 6)
Find the solution.
(4, 2)
Find the solution.
No Solution
Find the solution.
y = 2.2x + 46.7
From 1994 through 1997, the cost of owning and operating a car per mile increased by about 2.2 cents per year. In 1994 (year 0), it cost about 46.7 cents per mile. Write the equation that models the cost of owning and operating a car per mile to the years.
the salad's weight
Gabrielle makes a salad at a salad bar. The cost of the salad is calculated according to its weight. What is the independent variable?
{3, 1, -2, -4}
Identify the elements in the range of the function graphed.
the team's score
In hockey, a team's score depends on how many goals the team has score. What is the dependent variable?
the amount of money Warren's quartet earns
In order to earn extra money on the weekends, Warren's string quartet performs at wedding receptions. The longer the reception, the more money they earn. What is the dependent variable?
r = I/(pt)
Interest formula I = prt solve for r
$2
Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza for a total cost of $12.50. This is represented by the equation 3x + 4y = 12.50 Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50. This is represented by the equation 3x + 2y = 8.50. If x is number of cheese slices and y is the number of mushroom slices, what is the cost of the mushroom slices?
-4
Look at the graph of a function below and complete the statement. Range = y ≥ _____
the number of tickets the friends have won
Minh and her friends are at an arcade and are redeeming their tickets for prizes. The number of tickets they have won determines how many prizes they can get. What is the independent variable?
a = -2 b = 6 y-intercept (0, -2)
Name the a, b, and y-intercept for the exponential function f(x) = -2(6)^x
a = -2 b = 3 y-intercept (0, -2)
Name the a, b, y-intercept of f(x) = -2(3)^x
a = 2 b = 3 y-intercept (0, 2)
Name the a, b, y-intercept of f(x) = 2(3)^x.
a = -3 b = 0.8 y-intercept (0, -3)
Name the a, b, y-intercept of the exponential function f(x) = -3(0.8)^x
a = 0.8 b = 3 y-intercept (0, 0.8)
Name the a, b, y-intercept of the exponential function f(x) = 0.8(3)^x
a = 3 b = 0.8 y-intercept (0, 3)
Name the a, b, y-intercept of the exponential function f(x) = 3(0.8)^x
the number of hours Adon spends reading every day
Over summer vacation, Adon has to read a novel for English class. He has decided to spend the same amount of time reading every day. The number of days it will take him to finish the book depends on how many hours he spends reading every day. What is the independent variable?
L= (P - 2W)/2
Perimeter of a rectangle. P= 2L + 2W Solve for L
b= √(c²-a²)
Pythagorean Theorem a² + b² = c² Solve for b
y = 15x + 10
Renting a bike costs $15 per hour, plus $10 insurance. Write the equation that models the cost of renting a bike to the hours rented.
y = 28x + 10
Renting a canoe costs $10 plus $28 per day. Write the equation that models the cost of renting a canoe to the days rented.
m= (y - b)/x
Slope Intercept Form y = mx + b Solve for m
b= -a/m
Slope of a line in standard form is: m= -a/b Solve for b
x= (C - By)/A
Standard Form Ax + By = C Solve for x
As x--> positive infinity, y --> negative infinity. As x--> negative infinity, y --> 0.
State the end behavior for the exponential function f(x) = -6(2)^x
π = SA/(4r²)
Surface Area of a Sphere SA= 4πr² Solve for π
If f(x) is the parent function, what is the transformation if -4 f( x)
Th.e line is reflected over the y axis and rotated, steeper than the parent function.
y = 0.22x + 17.4
The US Bureau of the Census predicts that the population of Florida will be about 17.4 million in 2010 and then will increase by about 0.22 million per year until 2025. Write the equation that models the population as a function of the year since 2010.
Degree of a polynomial
The greatest degree of any term in the polynomial
If f(x) is the parent function, what is the transformation if the function is vertically stretched by a factor of 2 2*f(x)
The line is steeper than the parent function. Slope is 2.
If f(x) is the parent function, what is the transformation if f( x) - 2
The line is translated down 2 units.
If f(x) is the parent function, what is the transformation if f( x) +5
The line is translated or shifted up 5 units.
y = 12x + 120
The math club goes on a trip. Student tickets cost $12 each. Teachers go for free. The bus costs $120. Write a function that models the cost of the trip in terms of number of students attending.
y = 12x + 90
The math club goes on a trip. Student tickets cost $12 each. Teachers go for free. The bus costs $90. Write a function that models the cost of the trip in terms of number of students attending.
y = 15x + 90
The math club goes to an amusement park. Student tickets cost $15 each. Teachers go for free. The bus costs $90. Write a function that models the cost of the trip in terms of number of students attending.
the number of lifeguards scheduled to work
The number of lifeguards scheduled to work at the community pool on a given day varies depending on how many swimmers are expected to visit the pool on that day What is the dependent variable?
Degree of Monomial
The sum of the exponents of all of its variables.
Trinomial
The sum of three monomials
Binomial
The sum of two monomials
h = (3v)/A
Volume of a cone V = (Ah)/3 Solve for h
{-6, -4, 5, 8}
What is the domain of the function?
Time
What is the independent variable?
x<-3
What is the inequality for the graph?
x<-5
What is the inequality for the graph?
x<2
What is the inequality for the graph?
x<5
What is the inequality for the graph?
x>-3
What is the inequality for the graph?
x>2
What is the inequality for the graph?
x≤-3
What is the inequality for the graph?
x≤2
What is the inequality for the graph?
x≤5
What is the inequality for the graph?
x≥2
What is the inequality for the graph?
y ≤ 9
What is the range of the quadratic to the left?
(-1,-1)
What is the solution to the system?
(2,2)
What is the solution to the system?
(4,-4)
What is the solution to the system?
1
What is the value of the y coodinate of the solution to the system of equations x - 2y = 1 and x + 4y = 7?
2
What is the value of the y coordinate of the solution to the system of equations x + 2y = 9 and x - y = 3?
Solve -81 < 2(7x + 6) + 5
X > -7
36 = 8 + 4x
You have $36 to spend on posters for your bedroom. You buy 1 large poster for $8 and some small posters for $4. Write a function that models the cost of your shopping spree as a function of how many little posters you buy.
what is a domain?
a set of all the first numbers of the ordered pairs ,in the other words all x values.
range?
all of the y values of a relation
what is a relation?
any set of ordered pairs.
41
f(-7) = ?
56
f(-8) = ?
28
f(6) = ?
-2
find f(-1)
-5
find f(2)
Function or Not?( 2,4)(5,9)(12,15)
function
a= g+b+c
g = a - c - b (solve for a)
6
g(1) = ?
54
g(3) = ?
2
h(2.5) = ?
what is a function?
it is a rule is a rule that relates two qualities so that each input value corresponds to exactly one output value.
-2x + 3y = 27
linear
7y - 9 = 2x + 10
linear
x = 7
linear
y - 4 = 2(x + 7)
linear
y = 7x - 2
linear
y = x/2 - 9
linear
(n - 1)(n+1)
n^2 - 1
(n-7)(n-8)
n^2-15n+56
(n-8)^2
n^2-16n+64
(n+7)(n-8)
n^2-n-56
(n+2)(n^2+3n+6)
n^3+5n^2+12n+12
4y² = 2x
nonlinear
xy = 30
nonlinear
y = 2x² + 7x - 3
nonlinear
y = 4/x + 7
nonlinear
y = √x
nonlinear
y³ + 8 = x
nonlinear
function or not? ( 2,4)(2,9)(12,15)
not a function
(q+6)(q-4)
q^2+2q-24
(s-7)(s-3)
s^2-10s+21
x>-7
solve x/(-7) < 1
what is the vertical line test?
this test can be used to see if a graph represents a function , to be function a vertical line can only touch the graph at one point.
a = (u + 1)/-4
u = -4a - 1 (Solve for a)
a = (u-1)/-4
u = -4a+1 (solve for a)
x = (u + 5k)/4w
u = -5k + 4xw (solve for x)
x = (u+5k)/4
u = 4x - 5k (solve for x)
x= (6k-5)/u
ux + 5 = 6k (solve for x)
(13,29)
x + y = 42 y = 2x + 3
(10,-1)
x - y = 11 2x + y = 19
Solve 2 - 8x < 10 or 3x + 9 < -3
x > -1 or x < -4
Solve 2x - 10 > 0 or -5x - 6 ≥ -1
x > 5 or x ≤ -1
Solve 6x + 10 ≥ 70 or 4x - 5 < -29
x ≥ 10 or x < -6
x²
x(x)
(x^2+5)(x^3+2x+1)
x^5+7x^3+x^2+10x+5
x(x)
x²
(x²)(x³)
x⁵
(x⁴)(x³)
x⁷
1/x⁴
x⁻⁴
Infinite Solutions, same slope -4, same y-int 2
y = -4x + 2 4x + y = 2
opens down and moved up 1
y = -|x| + 1
No Solution, slope both 2 diff y-int
y = 2x + 5 y = 2x - 7
(2,3)
y = 5x - 7 -3x - 2y = -12
(2,1)
y = 6x - 11 -2x - 3y = -7
(0,0)
y = 8x -x + 6y = 0
(5,10)
y = x + 5 3x + y = 25
moved left 2 and down 1
y = |x + 2| - 1
moved left 4 and up 2
y = |x + 4| + 2
moved left 6 and up 8
y = |x + 6| + 8
moved right 2 and up 1
y = |x - 2| + 1
moved right 6 and up 8
y = |x - 6|+8
moved right 7
y = |x - 7|
If f(x) is the parent function, what is the transformation if it is reflected over the y-axis?
y-intercept stays same, slope has opposite sign/direction
x = (m-z)/3
z + 3x = m (solve for x)
a =b-z
z + a = b (solve for a)
x = (y-z)/m
z + mx = y (solve for x)
a = z - m + b
z = m + a - b (solve for a)
a = (z+b)/m
z = ma - b (solve for a)
x= zm - y
zm = x + y (solve for x)
domain of (13,25)(12,6)(2,8)?
{13,12,2}
domain of ( 2,4)(5,9)(12,15) ?
{2,5,12}
domain of (23,6)(23,9)(3,4)?
{23,3}
domain of (45,56)(45,3)(45,34)?
{45}
h = 2A/b
Area of a triangle. A= (1/2)bh Solve for h
7
Find f(4)
S= P/4
Perimeter of a square. P=4S. Solve for S