(61) Midterm Review (Fall22)(A2)

MMA-Midterm review

Multiple Choice

Name this Function:

• Linear

• Quadratic

• Absolute Value

• Cubed Root

Multiple Choice

Name this Function:

• Constant

• Quadratic

• Absolute Value

• Cubed Root

Multiple Choice

Name this Function:

• Constant

• Quadratic

• Square Root

• Cubed Root

Multiple Choice

The name of all the possible inputs of a function:

• Domain

• Range

Multiple Choice

The name of all of the possible outputs of a function:

• Domain

• Range

Multiple Choice

Write the equation that results if the parent absolute value function is shifted right 15 units, down 3 units, and reflected vertically.

• $$y=-\left|x-15\right|-3$$

• $$y=-\left|x+15\right|-3$$

• $$y=\frac{1}{2}\left|x+3\right|-15$$

• $$y=\frac{1}{2}\left|x-3\right|-15$$

• $$y=\left|-x-15\right|-3$$

Multiple Choice

Describe the transformation of the equation below from the absolute value parent function $$y=-2\left|x-3\right|+3$$  

• reflected over x axis, stretched by 2, right 3, up 3

• reflected over x axis, stretched by 2, left 3 up 3.

• reflected over x axis, shrunk by 2, right 3, up 3

• reflected over the x axis, shrunk by 2, left 3, up 3

Multiple Choice

What is the Range?

• y ≥ 6

• $$-\infty<y\le6$$  

• -10 ≤ y ≤ 6

• -10 ≤ x ≤ 6

Multiple Choice

What is the Domain?

• y ≥ 6

• $$-\infty<x<\infty$$  

• -10 ≤ y ≤ 6

• -10 ≤ x ≤ 6

Multiple Choice

What is the DOMAIN?

• [0, ∞)

• (-∞, 0)

• All real numbers

• {0, 1, 2, 3, 4,...}

Multiple Choice

What is the RANGE?

• (-∞, 0)

• (0, ∞)

• All real numbers

• {0, 1, 2, 3, 4,...}

Multiple Choice

What is the RANGE?

• all real numbers

• [1, ∞)

• (-∞, 1]

• none of these

Multiple Choice

• (-∞, ∞)

• [-2, 2]

• (-2, 2)

• [-5, 5]

Multiple Choice

Name the parent function and describe the transformation.

$$f\left(x\right)\ =\ \frac{1}{2}\left(x-6\right)^3\ +\ 4$$  

• Quadratic function vertically compressed by 1/2, shifted right 6 and up 4

• Quadratic function vertically stretched by 2, shifted right 6 and up 4

• Cubic function vertically compressed by 1/2, shifted right 6 and up 4

• Quadratic function vertically stretched by 2, shifted right 6 and up 4

Multiple Choice

What is the parent function and the transformed equation for the graph shown?

• Parent: $$f\left(x\right)\ =\ \sqrt[]{x}$$  

  New Function:

  $$f\left(x\right)\ =\ \sqrt[]{x\ -\ 1}\ +\ 2$$  

• Parent: $$f\left(x\right)\ =\ \left|x\right|$$  

  New Function:

  $$f\left(x\right)\ =\ \left|x-\ 1\right|\ +\ 2$$  

• Parent: $$f\left(x\right)\ =x^3$$  

  New Function:

  $$f\left(x\right)\ =\ \left(x-1\right)^3\ +\ 2$$  

• Parent: $$f\left(x\right)\ =\ \sqrt[]{x}$$  

  New Function:

  $$f\left(x\right)\ =\ 4\sqrt[]{x\ +\ 1}\ +\ 2$$  

Multiple Choice

Choose the equation that best matches the graphed function.

• $$f(x)=|x|+2$$  

• $$f(x)=|x|-2$$  

• $$f(x)=-|x|$$  

• $$f(x)=-|x|+2$$  

Multiple Choice

Describe the transformation

• left 2 up 5

• right 2 up 5

• left 2 down 5

• right 2 down 5

Multiple Choice

Describe the transformation from the parent graph

• Reflect over x, right 3, down 4

• Reflect over y, right 3, down 4

• Reflect over x, right 3, up 4

• Reflect over y, left 3, down 4

Multiple Choice

Solve $$-2\left(-7+x\right)+20\ge-32$$  on your paper before answering questions.

What is the first step on your paper?

• Multiply -2 times -7 and x. 

• Subtact -2 from -7.  

• Subtract 20 from each side. 

• Add 2 to both sides. 

Multiple Choice

Which figure shows the inequality x > -4?

• Figure 1

• Figure 2

• Figure 3

• Figure 4

Multiple Choice

Which inequality is represented by the words " more than"?

• <

• >

• ≤

• ≥

Multiple Choice

Which inequality is represented by the words " at least"?

• <

• >

• ≤

• ≥

Multiple Choice

solve 5( 6 + 3r) + 7 ≥ 127

• r ≤ 6

• r ≥ 6

• r ≤ -6

• r ≥ -6

Multiple Choice

Solve 28 − k ≥ 7(k − 4)

• k ≥ -7

• k ≤ -7

• k ≥ 7

• k ≤ 7

Multiple Choice

Solve:
7(x + 3) < 5x + 13

• x > -4

• x < 17

• x < -4

• x > -17

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

Find the inverse of
f(x) = 1/4x - 7

• f^-1(x) = 4x + 7

• f^-1(x) = -4x + 28

• f^-1(x) = -4x - 7

• f^-1(x) = 4x + 28

Multiple Choice

• Inverse Functions

• Not Inverse Functions

Multiple Choice

$$f\left(x\right)=\frac{6x}{5}+3$$   Find  $$f^{-1}\left(x\right)$$  

• $$\frac{5x-3}{6}$$  

• $$\frac{5\left(x-3\right)}{6}$$  

• $$\frac{5x}{6}-3$$  

• $$\frac{5x}{6}+3$$  

Multiple Choice

Find the inverse of  $$f(x)=10+7x$$  

• $$f^{-1}(x)=\frac{x-7}{10}$$

• $$f^{-1}(x)=\frac{x-10}{7}$$

• $$f^{-1}(x)=\frac{1}{10+7x}$$

Multiple Choice

If $$f\left(x\right)=-2x+3$$ and $$g\left(x\right)=-3x+2,$$ find $$f\left(2\right).$$    

• $$-1$$  

• $$3$$  

• $$-4$$  

• $$2$$  

Multiple Choice

If $$f\left(x\right)=-2x+3$$ and $$g\left(x\right)=-3x+2,$$ find $$g\left(-3\right).$$     

•   $$17$$  

• $$13$$   

• $$-13$$   

• $$11$$   

Multiple Choice

If $$f\left(x\right)=-2x+3$$ and $$g\left(x\right)=-3x+2,$$ find $$f\left[g\left(x\right)\right].$$      

•   $$-x+1$$   

• $$-2x^2$$    

• $$6x-1$$    

• $$5x+7$$    

Multiple Choice

If $$f\left(x\right)=x^2-1$$ and $$g\left(x\right)=4x-3,$$ find $$f\left(2\right).$$    

• $$\frac{2}{3}$$  

• $$-5$$  

• $$6$$  

• $$3$$  

Multiple Choice

If $$f\left(x\right)=x^2-1$$ and $$g\left(x\right)=4x-3,$$ find $$\left[f\circ g\right]\left(3\right).$$      

• $$43$$    

• $$91$$    

• $$80$$   

• $$26$$    

Multiple Choice

If $$f\left(x\right)=x^2-2,$$ $$g\left(x\right)=x+9$$ and $$h\left(x\right)=-3x,$$ find $$h\left[f\left(g\left(-2\right)\right)\right].$$         

• $$-123$$      

• $$-141$$       

• $$-165$$       

• $$134$$       

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

Solve the following inequality:

| 2w − 1 | < 11

• No Solution

• All Real Numbers

• −5 < w < 6

• −6 < w < 5

Multiple Choice

Solve the following inequality:

−5|x − 4| > −20

• x < 8 and x > 0

• x > 8 or x < 0

• all real numbers

• no solution

Multiple Choice

What is the vertex of the following function? $$y=|x-3|+1$$  

• $$(2,3)$$  

• $$(-3,1)$$  

• $$(2,-3)$$  

• $$(3,1)$$  

Multiple Choice

Solve for x
l 2x−1 l = 9

• x = 5 and x =-4

• x = 5 and x = -5

• Only x = 5

• No Solution

Multiple Choice

Solve for x
l x−6 l + 4= 10

• x = 12 and x = 0

• x = 3 and x = -3

• x = -12 and x = 0

• No Solution

Multiple Choice

Solve for x
3 l 4w−1 l −5 = 10

• x = 1.5 and x =-1

• x = -1.5 and x = 1

• x =1 and x = -1

• No Solution

Multiple Choice

What is the value of the x-coordinate to the solution to this system of linear equations?

2x + 3y = 15 and -x + 3y = 3

• 3

• -3

• 6

• 4

Multiple Choice

What is the value of the y-coordinate in this system of linear equations?

6x + 10y = -32 and 6x + 9y = -27

• y = 5

• y = 0

• y = -5

• y = 1

Multiple Choice

solve by substitution: y=3x+14
y=-4x

• y=3

• y=1

• y= - 2

• y=4

Multiple Choice

What is the solution to this system of equations?

• (4, -1)

• (-1, 4)

• (-4, 1)

• (-4, -1)

Multiple Choice

Solve the system given:
3x - y = 7
2x + y = 3

• (-1,2)

• (5,4)

• (4,5)

• (2,-1)

Multiple Choice

Solve the system.

• (3, -2, 4)
• (2, -3, 1)
• (-3, 2, -1)
• Infinitely many solutions

Multiple Choice

Solve the system.

• (2, -2, 3)

• (2, 1, 4)

• (-2, 2, -3)

• No Solution

Multiple Choice

Solve the system. 

• (5, -6, 3)

• (2, 3, -1)

• (-4, 2, 5)

• No Solution

Multiple Choice

Determine the solution to the given linear-quadratic function.

• (0, 0)
• (3, 0)
• (2, -3)
• (-3, 2)

Multiple Choice

What are the solutions to the system:
y = x² + 3x - 5
y = x + 3

• (-4, 2) and (-1, 5)

• (-4, -1) and (2, 5)

• (2, -1 and (-4, 5)

• (-4, 1) and (2, -1)

Multiple Choice

Determine the number of solutions to the given linear-quadratic system.

• 0 solutions

• 1 solution

• 2 solutions

• 3 solutions

Multiple Choice

Find the solution.

• (2,3) and (3,4)

• (-3,-15) and (4,-8)

• (-3,10) and (8,4)

• (-8,3) and (-4,10)

Multiple Choice

How many solutions does this system of equations have?

• one solution

• two solutions

• no solution

• infinitely many solutions

Multiple Choice

$f\left(x\right)=5x-12$ What is $f\left(-4\right)$

• -32

• -3

• -12

• 3

Multiple Choice

$$Given\ h\left(x\right)=3x^2-2x+8\ what\ is\ h\left(2\right)?$$  

• 13

• 8

• 16

• answer not here

Multiple Choice

$$\left(n^3-3n-5n^2\right)+\left(n^2+3+2n^3\right)$$  

• $$-n^3-4n^2+n+3$$  

• $$3n^3-4n^2+n+3$$  

• $$2n^3-4n^2+n+3$$  

• $$3n^3-4n^2-3n+3$$  

Multiple Choice

$$\left(4m-4m^3+m^2\right)-\left(m^3-5-2m\right)$$  

• $$-5m^3-2m^2+6m+9$$  

• $$-5m^3+m^2+6m+9$$  

• $$-5m^3-2m^2+m+9$$  

• $$-5m^3+m^2+6m+5$$  

Multiple Choice

(4x - 1)(5x−2)

• 20x² + 3x − 2

• 20x² − 11x + 5

• 20x² − 13x + 2

• 20x² − 3x − 2

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

Divide

$$\frac{10x^8y^5}{4x^2y^5}$$  

• $$6x^6y$$  

• $$\frac{5x^6}{2}$$  

• $$\frac{5x^6y}{2}$$  

• $$6x^6$$  

Multiple Choice

Divide

$$\frac{-4a^{7\ }-\ 6a^5}{2a^3}$$  

• $$2a^{4\ }+3a^2$$  

• $$4a^{4\ }-\ 4a^2$$  

• $$-2a^{7\ }-\ 3a^5$$  

• $$-2a^{4\ }-3a^2$$  

Multiple Choice

Divide

$$\frac{-20p^2-16p}{-4p}$$  

• 5p² - 16p

• 5p + 4

• 5p - 4

• 5p + 4p

Multiple Choice

Factor
d² - 10d + 25

• (d + 5) (d - 5)

• (d - 15) (d + 10)

• (d + 5) (d - 20)

• (d - 5) (d - 5)

Multiple Choice

Factor:x² - 25

• ( x + 5 ) ( x - 5 ) 

• ( x - 5 ) ( x - 5 ) 

• ( x + 5 ) ( x + 5 ) 

• Prime

Multiple Choice

Factor completely: 2x²+22x+60

• (2x+10)(x+6)

• (x+5)(x+6)

• 2(x+1)(x+30)

• 2(x+5)(x+6)

Multiple Choice

Factor completely.

$$2x^2-3x-14$$  

• $$\left(x+7\right)\left(2x-3\right)$$  

• $$\left(2x+2\right)\left(x-7\right)$$  

• $$\left(2x-7\right)\left(x+2\right)$$  

• $$\left(x-14\right)\left(x+1\right)$$  

Multiple Choice

Factor Completely

$$x^2-49$$  

• $$\left(x+7\right)\left(x-7\right)$$  

• $$7\left(x-7\right)$$  

• $$\left(x-7\right)\left(x-7\right)$$  

• $$x\left(x-7\right)$$  

Multiple Choice

(3 + 2i) + (4 - 5i)

• 7 + 7i

• 1 - 3i

• 1 - 7i

• 7 - 3i

Multiple Choice

(-7 + 9i) + (2 - 10i)

• -5 + i

• -5 - i

• -9 + 1

• 9 - i

Multiple Choice

(4 - 2i) - (3 + 6i)

• 7 - 4i

• 1 + 4i

• 1 - 8i

• 7 - 8i

Multiple Choice

The expression (2 + 3i)² is equal to

• -5

• -5 + 12i

• 13

• 13 + 12i

Multiple Choice

Multiply
(2i)(3i)

• 5i

• -5

• 6i

• -6

Multiple Choice

Simplify $$\sqrt[]{-1}$$  

• 1

• $$\pm1$$  

• i

• 1 + i

Multiple Choice

$$i^9$$  

• $$i$$  

• $$-i$$  

• -1

• 1

Multiple Choice

$$i^6$$  

• $$i$$  

• -1

• $$-i$$  

• 1