Algebra Non Linear Functions Review

Algebra Non Linear Functions Review

Absolute Value and Square Root Solving and Graphing

Multiple Select

Select all that apply. (May have more than one answer)

Which letter(s) does the function have?

f(x) = 4|x-2|+1

• H

• A

• K

• None

Multiple Select

Select all that apply. (May have more than one correct answer)

f(x) = |x - 6| + 2

• Horizontal translation right 6 units

• Horizontal translation left 6 units

• Vertical translation up 2 units

• Vertical translation down 2 units

Multiple Choice

What is the vertex of the function?

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

• (-3, -2)

• (3, -2)

• (3, 2)

• (-3, 2)

Multiple Choice

Select the correct set of transformations.

f(x) = 1/3 |x + 4| - 2

• Horizontal translation left 4 units

  Vertical shrink by a factor of 3 units

  Vertical translation down 2 units

• Horizontal translation right 4 units

  Vertical shrink by a factor of 3 units

  Vertical translation down 2 units

• Horizontal translation left 4 units

  Vertical shrink by a factor of 3 units

  Vertical translation up 2 units

• Horizontal translation left 4 units

  Vertical stretch by a factor of 3 units

  Vertical translation down 2 units

Multiple Choice

Which function is graphed?

• f(x) = -3|-x + 1| + 4
• f(x) = -|x - 1| + 4
• f(x) = -5|x + 1| + 4
• f(x) = -3|x - 4| + 1

Multiple Choice

Which function is graphed?

• f(x) = 2|x - 5|
• f(x) = |x - 5|
• f(x) = |x - 5| + 5
• f(x) = |x| + 5

Multiple Choice

Which function is graphed?

• f(x) = -|2x - 3| + 5

• f(x) = -|x + 5| - 3

• f(x) = -|2x + 4| + 5

• f(x) = -2|x + 5| - 3

• f(x) = -2|x + 3| + 5

Multiple Choice

Which function is graphed?

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

Multiple Choice

True or False: Is x = 4 a solution to |x + 5| = -9

• True
• False

Multiple Choice

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

• Absolute value is talking about numbers so it must be positive.
• Absolute value does not always have to be positive.
• Absolute value is like a clock it has only positive numbers.
• Absolute value is talking about distance, distance is always measured by positive numbers.

Multiple Choice

Solve for x
l 5x l = 40

• x = 8 and x =-8
• x = 35 and x = -35
• Only x = 8
• No Solution

Multiple Choice

-|−2r − 1| = 11

• {-6,5}
• {5,-6}
• -6
• No Solution

Multiple Choice

Solve for x
l 2x−1 l +4 = 8 

• x = 2.5 and x = -1.5
• x = 2 and x = -1
• x = -2 and x = 9
• No Solution

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
2 lx−4l+8=18

• x = 9 and x =-1
• x = 1 and x = -9
• x= 4 and x = -2
• No Solution

Multiple Select

Identify each value that is a solution to the indicated inequality.  $\left|x\right|-2\le0$   

•  $-4$   

•  $-2$  

•  $0$  

•  $1$  

•  $4$   

Multiple Select

Select all of the options that show an AND statement.

• The interval $\left(-2,\ 2\right)$

• $\left|x+6\right|>2$

• $\left|x+6\right|<2$

Multiple Choice

Solve.
-5|x - 4| < 20

• x < 8 and x > 0
• x > 8 or x < 0
• all real numbers
• no solution

Multiple Choice

Solve.
-5|x - 4| > 20

• x < 8 and x > 0
• x > 8 or x < 0
• all real numbers
• no solution

Multiple Choice

Solve:
3 | 2x + 7| - 7 < -4

• x < -3 and x > -5/3
• x < -3 and x > -4
• all real numbers
• no solution

Multiple Choice

Solve:
 |x + 3| > 8

• x > 5 or x < -11
• x > 5
• all real numbers
• no solution

Multiple Choice

Identify the absolute value inequality that would generate the given graph.

•  $\left|x+12\right|>5$  

•  $\left|x+12\right|\ge5$  

•  $\left|x+12\right|<5$  

•  $\left|x+12\right|\le5$  

Multiple Choice

Identify the inequality with a solution represented by the given graph.

Multiple Choice

Solve using square roots.
4m² - 100 = 0

• m=25, -25
• m=96
• m=5, -5
• m=-96

Multiple Choice

Solve using square roots.
5b² - 4 = 41

• b = 9, b = -9
• b = 3, b = -3
• b = 8, b = -8
• no solution

Multiple Choice

Solve:  $7x^2=-21$  

•  $x=\pm\sqrt{3}$  

• No real solution

•  $x=\pm2\sqrt{7}$  

•  $x=\pm\sqrt{14}$  

Multiple Choice

Solve for x

3x² - 27 = 0

• x = 4.9, -4.9

• x = 9, -9

• x = 3, -3

• No solution

Multiple Choice

Solve for x

x² = 64

• x = 8, -8

• x = 32, -32

• x = 4, -4

• No real solution

Multiple Choice

Solve

• -5
• 5
• 10
• 25

Multiple Choice

• x = 2
• x = 4
• x = 7
• x = 9

Multiple Choice

Solve.

• no solution
• 6
• 3
• 4

Multiple Choice

• x = 5
• x = 10
• x = -9
• x = -5

Multiple Choice

• x = 49
• x = 53
• x = 45
• x = 18

Multiple Choice

What are the transformations of this functions compared to the parent function?

• Shifted down 2
• Shifted up 2
• Shifted left 2
• Shifted right 2

Multiple Choice

What are the transformations for the graph of
the parent function f(x) = √x  to the function above 

• Vertical Stretch by a factor of 2; translated down 5 units 
• Shifted right 2 units and down 5 units 
• Vertical stretch by a factor of 2; translated left 5 units
• Vertical stretch by a factor of 2; translated right one unit 

Multiple Choice

What are the transformations of this functions compared to the parent function?

• Shifted down 2

• Shifted up 2

• Shifted left 2

• Shifted right 2

Multiple Choice

Match the correct equation with the given graph.

• y = √(x) + 2
• y = √(x) - 2
• y = √(x + 2)
• y = √(x - 2)

Multiple Choice

What function best describes this graph?

• f(x)= -√(x+4) -2
• f(x)= √(x-4) -2
• f(x)= -√(x-4) -2
• f(x)= √(x+4) +2

Multiple Choice

Which function matches the graph?

• A

  f(x) = ∛(x + 3) + 2

• B

  f(x) = − ∛(x - 3) + 2

• C

  f(x) = ∛(x - 3) + 2

• D

  f(x) = ∛(x - 2) + 3

Multiple Choice

What is the equation of the graph?

• y = √(x - 3)
• y = √(x) + 3
• y = √(x - 5) + 4
• y = √(x + 5) + 4

Multiple Choice

Which function matches the graph?

• A

  f(x) = − ∛(x + 3) − 1

• B

  f(x) = − ∛(x - 3) − 1

• C

  f(x) = ∛(x + 3) − 1

• D

  f(x) = ∛(x - 1) + 3

Multiple Choice

• y = 2 √(x) - 4
• y = - √(x - 4)
• y = 2 √(x)
• y = 2 √(x) + 4

Multiple Choice

What is the equation of the graph?

• y = -√(x + 5)
• y = √(x) - 2
• y = √(x - 3)
• y = √(x) + 3

Multiple Choice

What is the equation of the graph?

• y = √(x - 3)

• y = √(x) + 3

• y = √(x - 5) + 4

• y = √(x + 5) + 4