Final Exam Revision

Final Exam Revision

by Sahel Otoom

Multiple Choice

Which mapping diagram is not a function?

Multiple Choice

Describe the interval shown using an interval notation?

•  [−3, +∞)

•  (−3, +∞]

•  [−3, 4]

•  (−3, +∞)

Multiple Choice

What is the domain?

• all real numbers
• 1<x<6
• {1,3,4,6}
• {-2,2,5}

Multiple Choice

What is the range?

• {-2,2,5}
• {1,3,5,6}
• all real numbers 
• -2<y<5

Multiple Choice

What is the domain of this graph?

•  x  >  0

• (−∞,∞)

•  x  <  0

Multiple Choice

What is the domain?

• {-2, -1, 0, 1, 8}
• {3, 5, 7 , 9, 0}
• {-2, -1, 0, 1, 3, 5, 7, 8, 9}
• {-2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

Multiple Choice

What is the range?

• {-3, -1, 2, 4}
• {0, 4, 7} 
• {0, 4, 4, 7}
• {7, 4, 0}

Multiple Choice

For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.

• D: {1, -3, -4,}
  R: {0, 1, 2, -4}
• D:{-4, 0, 1, 2}
  R:{-4, -3, 1}
• D:{0, 1, 2, 3, 4}
  R:{1, -3, -4}

Multiple Choice

Evaluate f(-2) if f(x) = x²+ 3

• -1

• 1

• 7

• -7

Multiple Choice

What is the domain of a relation?

• the set of all x-values

• the set of all y-values

Multiple Choice

Which is the set of all y-values or the outputs?

• Domain

• Range

• Relation

• Function

Multiple Choice

What is the range of the mapping?

• {1, 2, 4}

• {0, 1, 2, 3}

• {0, 3}

• {1, 4}

Multiple Choice

What is the range?

• -4 < x ≤ 5

• -4 ≤ x < 5

• -3 < y < 3

• -3 ≤ y ≤ 3

Multiple Choice

What is the DOMAIN of this graph?

• -4 ≤ x ≤ 3

• -1 ≤ x ≤ 4

• 4 < x < 3

• -1 < x < 4

Multiple Choice

What is the domain in Interval notation?

• [ -2 , 2 ]

• [ 4 , -4 ]

• (-2 , 2 )

• (4 , -4 )

Multiple Choice

What is the domain in inequality notation?

• [ -2 , 2 ]

• [ 4 , -4 ]

• -2 ≤ x ≤ 2

• 4 ≥ y ≥ -4

Multiple Choice

What is the range in interval notation?

• [ -2 , 2 ]

• [ 4 , -4 ]

• -2 ≤ x ≤ 2

• 4 ≥ y ≥ -4

Multiple Choice

What is the domain in interval notation?

• ( -5 , 5 )

• [-2 , -4 )

• -5 < x < 5

• -2 ≥ y > -4

Multiple Choice

What is the domain in interval notation?

• [ -2 , 2 )

• ( 5 , 1 ]

• -2 ≤ x < 2

• 5 > y ≥ 1

Multiple Choice

What is the range in interval notation?

• [ -2 , 2 )

• ( 5 , 1 ]

• -2 ≤ x < 2

• 5 > y ≥ 1

Multiple Choice

What is the domain in interval notation?

• ( -4 , 4 )

• [ 1 , -3 )

• [-4, 4]

• (-3, 1]

Multiple Choice

What is the domain in inequality notation?

• ( -4 , 4 )

• [ 1 , -3 )

• -4 < x < 4

• 1 ≥ y > -3

Multiple Choice

How many x-intercepts are there for the function’s graph?

• 4

• 6

• 8

• 10

Multiple Choice

 What are the zeros of the function?

• 4,8,12,16 and 20

• -2,0,and 2

• 2,6,10,14,18 and 22

• 18 and 22

Multiple Choice

What are the zeros of the function?

• 1, and 2.

• -2, -1, and 2.

• -2, 1, and 2.

• -2, 1, and 3.

Multiple Choice

A function is decreasing on an interval when its graph rises from left to right.

• True

• False

Multiple Choice

What is the inverse of the points(1,3) (2,4) (6,8).

• (3,1)(4,2)(8,6)

• (-3,-1)(-4,-2)(-8,-6)

• (1,3)(2,4)(6,8)

• (-1,-3)(-2,-4)(-6,-8)

Open Ended

Type the missing values in the diagram for the inverse of the function, mapping the range to the domain.

Multiple Choice

The student council set its members on four field trips during the school year.  The number of buses needed to transport the members on each trip is a function of the number of members who went on the trip.  This function consists of only the ordered pairs (52, 3), (72, 4), (86, 5), and (105, 6).  What is the inverse for this situation?

• (52, 3), (72, 4), (86, 5), and (105, 6).

• (3, 52), (4, 72), (5, 86), and (6, 105).

• (-52, 3), (-72, 4), (-86, 5), and (-105, 6).

• (52,- 3), (72,- 4), (86, -5), and (105,- 6).

Multiple Choice

The inverse of the function f(x) is written as ...

• f ^-1(x)

• f ²(x)

• f '(x)

• f ⁺(x)

Multiple Choice

The inverse has been reflected over which line?

• y = x

• y =1

• y = 0

• y = x + 1

Multiple Choice

Find the inverse of f(x) = -4x - 12

• f^-1(x) = 4x - 3

• f^-1(x) = -1/4x - 3

• f^-1(x) = 1/4x + 3

• f^-1(x) = -4x - 3

Multiple Choice

When finding the inverse of a relation, 1st you replace f(x) with y 2nd switch the x's and y's What do you do next?

• solve for y

• replace y with f^-1(x)

• solve for x

• find the greatest common factor

Multiple Choice

A. MANUFACTURING  The fixed costs for manufacturing one type of stereo system are $96,000 with variable cost of $80 per unit. The total cost f (x) of making x stereos is given by f(x) = 96,000 + 80x. Explain why the inverse function

f –1(x) exists. Then find f –1(x).

• $$f^{-1}\left(x\right)=\frac{1}{80}x-1200$$  

• $$f^{-1}\left(x\right)=\frac{1}{80}x+1200$$  

• $$f^{-1}\left(x\right)=\frac{1}{80}x-20$$  

• $$f^{-1}\left(x\right)=2x+1200$$  

Multiple Choice

EARNINGS  Ernesto earns $12 an hour and a commission of 5% of his total sales as a salesperson. His total earnings f (x) for a week in which he worked 40 hours and had a total sales of $x is given by f (x) = 480 + 0.05x. Explain why the inverse function f –1(x) exists. Then find f –1(x).

• $$f^{-1}\left(x\right)=20x-9600$$  

• $$f^{-1}\left(x\right)=40x+30$$  

• $$f^{-1}\left(x\right)=0.05x+840$$  

• $$f^{-1}\left(x\right)=x$$  

Multiple Choice

You can find the inverse of a function by switching the x-values (domain) and y-values (range) in each ordered pair.

• True 

• False

Multiple Choice

What is the reason that absolute value is always written as a positive?

• Absolute value is like a clock it has only positive numbers.

• Absolute value is talking about numbers so it must be positive.

• Absolute value does not always have to be positive.

• Absolute value is talking about distance, distance is always measured by positive numbers.

Multiple Choice

Is absolute value always positive?

• yes

• no

Multiple Choice

Evaluate $$\left|2x\right|+1$$  for

x = -1

• 2

• 3

• -2

• -3

Multiple Choice

Evaluate  $$-2\left|2x-4\right|+6$$  for  $$x=-2$$  

• -10

• 10

• -12

• 12

Multiple Choice

The Domain of  $$f\left(x\right)=\left|x\right|\ is$$  :

• $$\left(-\infty,\infty\right)$$  

• $$\left(0,\infty\right)$$  

• $$\left(2,\infty\right)$$  

• $$\left(-4,4\right)$$  

Multiple Choice

The Range of  $$f\left(x\right)=\left|x\right|\ is$$  :

• $$\left(-\infty,\infty\right)$$  

• $$\left[0,\infty\right)$$  

• $$\left(2,\infty\right)$$  

• $$\left(-4,4\right)$$  

Multiple Choice

The Range of  $$f\left(x\right)=\left|x-3\right|+2\ \ is$$  :

• $$2\le y<\infty$$  

• $$2<y<\infty$$  

• $$2\le x<\infty$$  

• $$\left(-4,4\right)$$  

Multiple Choice

What is the range of the absolute value function?

•  (- $$\infty$$  , 4]

• [4, $$\infty$$  )

• $$\left(-\infty,\infty\right)$$  

• [0, $$\infty$$  )

Multiple Choice

What is the value of h?

f(x) = |x + 4| - 2

• -2

• 2

• 4

• -4

Multiple Choice

What is the value of k?

f(x) = 4|x +2| - 3

• 3

• -3

• 2

• -2

Multiple Choice

Write an absolute value function given the following transformations:

Horizontal shift left 1 unit

Vertical shift down 9 units

• f(x) = |x + 1| - 9

• f(x) = |x - 1| - 9

• f(x) = |x - 1| +9

• f(x) = |x + 9| - 1

Multiple Choice

Describe the transformation of the equation below from the parent function of

y = IxI ,

y = I x + 2 I - 5

• Left 2 up 5

• Right 2 up 5

• Left 2 down 5

• Right 2 down 5

Multiple Choice

Before (Warm Up)

What is the vertex of $$f\left(x\right)=6\left|x-1\right|-2$$  ?

• (6,-1)

• (-1,-2)

• (1,-2)

• (1,2)

Solving Absolute Value Equations

by Sahel Otoom

Multiple Choice

Solve for X

|X|=7

• X= 7

• X= -7

• X= 7 and X= -7

• No Solution

Multiple Choice

Solve for X

|X| = -3

• X= 3 and X= -3

• X= 3

• X= -3

• No Solution

Multiple Choice

Solve for x

-6|-2x - 7| = -18

• {-5,-2}

• {5,-2}

• {-5,2}

• {5,2}

Multiple Choice

solve for z.

|3z|+1=10

• {-3,3}

• {3,4}

• {-3,6}

• {-2,3}

Multiple Choice

Solve

∣ 2x + 9 ∣ = 15

• { -6,3}

• { -12,6}

• {3}

• { -12,3}

Multiple Choice

Solve

2| x – 3 |+8= 8

• 3

• -3

• {-3, 3}

• no solution

Multiple Choice

How many solutions does the equation have?

6|r - 4| = -18

• no solution

• one solution

• two solutions

• infinity many solutions

Multiple Select

An absolute value equation can have which numbers of solutions?

(select all that apply)

• No Solution

• 1 Solution

• 2 Solutions

• 4 Solutions

• 5Solutions

Multiple Choice

The graphs here represent the two sides of an absolute value equation. How many solutions does the equation have?

• No solutions

• 1 solution

• 2 solutions

• 3 solutions

Multiple Choice

The graphs here represent the two sides of an absolute value equation. How many solutions does the equation have?

• No solutions

• 1 solution

• 2 solutions

• 3 solutions

Multiple Choice

The graphs here represent the two sides of an absolute value equation. How many solutions does the equation have?

• No solutions

• 1 solution

• 2 solutions

• 3 solutions

Multiple Choice

For an absolute value equation to have ONE solution, which of the following should be true?

• |__| = +

• |__| = -

• |__| = 0

Multiple Choice

For an absolute value equation to have TWO solution, which of the following should be true?

• |__| = +

• |__| = -

• |__| = 0

Multiple Choice

For an absolute value equation to have NO solution, which of the following should be true?

• |__| = +

• |__| = -

• |__| = 0

Multiple Choice

• A

• B

• C

• D

Multiple Choice

Complete the explanation of the error. The student replaced the absolute value with two equations using the positive and negative values of the number on the other side of the equal sign. However, this number was negative.

• An absolute value cannot be equal to a negative number. The equation has no valid solution.

• He should have only used the negative choice, so only

  13/4

  is a valid solution.

• He should have only used the positive choice, so only 27/4 is a valid solution.

• There is no error, so both

  13/4

  and

  27/4

  are valid solutions.

Multiple Choice

Terry is trying to place a satellite dish on the roof of his house at the recommended height of 36 feet. His house is 40 feet

wide, and the height of the roof can be described by the function

h(x) = −32|x − 20| + 30,

where x is the distance along the width of the house. Complete the absolute-value equation and determine where Terry should place the dish.

The satellite dish needs to be 36 feet above the ground.

• Terry should place the satellite dish at one of the edges of the roof,

  x = 0 feet

  or

  x = 40 feet.

• Terry should place the satellite dish at

  x = 10 feet

  or

  x = 30 feet.

• Terry should place the satellite dish at the peak of the roof,

  x = 20 feet.

• There is no place on the roof that is 36 feet high.

Multiple Select

For what type of real-world quantities would the negative-valued answer for an absolute-value equation not make sense? Select all that apply.

• Length

• Bank account balance

• Time

• Distance

Multiple Choice

Challenge

This absolute value equation has nested absolute values.

||2x + 9| − 7| = 16

• The solution is

  x = −16 or x = 7.

• The solution is

  x = −16 or x = -7.

• The solution is

  x = 16 or x = 7.

• No solutions

Solving Absolute value inequalities

by Sahel Otoom

Multiple Choice

| x | ≤ 3.5

• No Solution
• All Real Numbers
• -3.5 ≤ x ≤ 3.5
• x ≤ -3.5  or  x ≥ 3.5

Multiple Choice

| 2w - 1 | < 11

• No Solution
• All Real Numbers
• -5 < w < 6
• -6 < w < 5

Multiple Choice

| x + 3 | ≤ 2

• No Solution
• All Real Numbers
• -5 ≤ x ≤ -1
• 1 ≤ x ≤ 5

Multiple Choice

3 | 2t - 3 | - 5 > 16

• No Solution
• All Real Numbers
• t < -2  or  t > 5
• -2 < t < 5

Multiple Choice

3 | d + 1 | - 7 ≥ -1

• No Solution
• All Real Numbers
• d ≤ -3  or  d ≥ 1
• -1 < d < 3

Multiple Choice

Solve the following inequality:

| x − 2 | > 3

• 2 < x < 10

• x < 2 or x > 10

• −1 < x < 5

• x < −1 or x > 5

Multiple Choice

Add the polynomials (x-2) and (x²+3)

• x²+x+1
• x³+5
• x³+1
• x³-1

Multiple Choice

Combine like terms to simplify:
 (5x + 2) + (4x + 5)

• 9x -7
• -9x-11
• 9x+7
• x+7

Multiple Choice

Add the polynomials.
(2x + 5y) + (3x - 2y)

• 3x + 5y
• 5x + 3y
• 5x + 7y
• 7xy + 1xy

Multiple Choice

Simplify the expression.
(4a³ - 8a - 4a²) + (7a³ - 7 - 6a)

• 11a³ - 4a² - 14a - 7 
• 5a³ - 4a² - 14a - 7 
• 5a³ - 4a² - 20a - 7 
• 5a³ - 9a² - 20a - 7

Multiple Choice

What is the standard form of the polynomial:
 9x² + 5x + 27 + 2x³

• 27 + 5x + 9x² + 2x³
• 9x² + 5x + 2x³ + 27
• 9x² + 5x + 27 + 2x³
• 2x³ + 9x² + 5x + 27

Multiple Choice

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

• 3y³ + 7y² - 4y + 3
• 4y² + 3y³ - y + 3
• -y⁴ + 2y³ -y - 4
• 4y³ + 3y² -3y + 1

Multiple Choice

(x³-x²+4) - (3x³-2x²+3)

• -2x³-3x²+7
• -2x³+x²+1
• 2x³-3x³-1
• 4x³-3x²+7

Multiple Choice

Simplify the expression. (4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

• -8n² - 8n + 3 
• -7n² - 8n + 3 
• -6n² - 8n + 3
• -7n² - 4n + 3

Multiple Choice

The length of a rectangle is (2x + 1). The width of the rectangle is (x²+ 2x - 1). Which expression represents the perimeter of the rectangle?

• x³ + x + 3

• 2x² + 8x

• 2x³ + 5x² -1

• x³ + 5x² -1

Multiple Choice

Find the Volume of the rectangular prism whose length is (3m - 2), height is (m + 4), and width is (5m³)

• 15m⁵ + 50m⁴ - 40m³

• 3m² + 10m - 8

Multiple Choice

Warm up

Find the area of a rectangle with length (x - 5) and width (3x + 1).

• 3x²+16x-5
• 3x²-14x+5
• 3x²-14x-5

Multiple Choice

Write the expanded (general) form of the product (x+3)(x+6).

• x²+18x+9

• x²+9x+18

• x²+18x+18

Multiple Choice

What does FOIL stand for?

• Flogging Outlawed in London
• Fans On in Landing
• First Outside Inside Last
• Fishing Only in Lakes

Multiple Choice

(x + 5)² 

Hint: try (x + 5)(x + 5)

• x² + 25
• x² + 10x + 25
• x² + 10 x + 10
• x² + 10

Multiple Choice

Find the product:
(3x – 1)(x + 5) 

• 3x² + 4x + 5
• 3x² + 4x - 5
• 3x² + 14x + 5
• 3x² + 14x - 5

Multiple Choice

A biologist has found that the number of branches on a certain rare tree in its first few years of life can be modeled by the polynomial $$b\left(y\right)=4y^2+y$$   The number of leaves on each branch can be modeled by the polynomial $$l\left(y\right)=2y^3+3y^2+y$$   where y is the number of years after the tree reaches a height of 6 feet. Write a polynomial describing the total number of leaves on the tree.

• 8y ⁵ + 14y ⁴ + 7y ³ + y ²

• 20y ⁵ + 14y ⁴ + 7y ³ + y 

• 8y ⁵ + 7y ⁴ + 7y ³ + 9y ²

Multiple Choice

Select the coefficients of the 5th Row in Pascal's Triangle

• 1;3;3;1

• 1;4;6;4;1

• 1;5;10;10;5;1

• 1;6;15;20;15;6;1

Multiple Choice

Choose the right Pascal's triangle

Multiple Choice

Which row of Pascal's Triangle would you use to expand (x+y)³?

• 1
• 1  1
• 1  2  1
• 1  3  3  1

Multiple Choice

Expand the expression using the Binomial Theorem.

(2x+5)⁴

• 2x⁴ + 40x³ + 300x² + 1000x +625

• 16x⁴ + 160x³ +600x² +1000x + 625

• 16x⁴ + 1000x³ + 600x² + 160x +625

Multiple Choice

How many rows in The Pascal's triangle?

• 7

• 8

• 100

• Infinite

Multiple Choice

What is the Binomial expansion of (x + 1)⁵ ?

• x⁵ + 5x⁴ + 10x³ + 10x² + 5x + 1

• x⁵ + 5x⁴ + 15x³ + 15x² + 5x + 1

• x⁵ + 6x⁴ + 15x³ + 15x² + 6x + 1

Multiple Choice

A group of engineers in the city of Abu Dhabi is working on a plan for the city's

streets, according to the expression  (1 + 4x)³ 

Which of the expression is equivalent to the binomial in the diagram?

• 1 + 12x + 12x² + 4x³

• 1 + 12x + 48x² + 64x³

• 1 + 3x + 3x² + x³

Multiple Choice

Ahmed has 7 unique bracelets and is trying to decide which 3 to wear on a date. Use Pascal's Triangle to find the number of different combinations of 3 bracelets that Ahmed could choose from the 7 he owns?

• 35

• 25

• 40

• 100

Multiple Choice

Find the 2nd term in the expansion of 
(2b + 1)³

• 12b²
• 6b
• 8b³
• 4b²

Multiple Choice

Find the 4th term in the expansion of (4x-3)⁵.

• 5760
• -4320x²
• 5760x³
• -4320

Multiple Choice

What is row 5 of Pascal's Triangle?

• 1, 5, 10, 10, 5, 1

• 1, 7, 21, 35, 35, 21, 7, 1

• 1, 5, 10, 5, 1