Radical to Exponential and Back

Radical Equations Unit Test

Composition of Functions

Multiple Choice

f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))

• 19
• 23
• -10
• None of these.

Multiple Choice

If f(x) = 5x and g(x) = 2x-1,

what is the composition f(g(x)) ?

• 10x-1

• 10x-5

• 5x²-1

• 5x²-5

Multiple Choice

If f(x) = 3x-1 and g(x) = x²+2,

what is (f ° g)(x) ?

• 3x² +5

• x² +1

• 3x² +1

• 3x² +6

Inverse Functions

Multiple Choice

Are the following inverses of each other? Use composition of functions. fog(x) and gof(x)

• True

• False

Multiple Choice

f(x) = -4x - 12

What is f^-1(x)?

• f^-1(x) = 4x - 3

• f^-1(x) = -1/4x - 3

• f^-1(x) = 1/4x + 3

• f^-1(x) = -4x - 3

Multiple Choice

• A
• B
• C
• D

Transformations

Multiple Choice

Which graph represents the function?

Multiple Choice

Identify the Transformations. 

• Down 2
• Up 2
• Reflection and stretch by 2
• Reflection and down 2

Multiple Choice

If f(x) = x³ is changed to f(x) = - (x + 3)³ + 2, how is the graph transformed?

• 3 units right, 2 units up, reflected across the y-axis
• 3 units right, 2 units up, reflected across the x-axis
• 3 units left, 2 units up, reflected across the y-axis
• 3 units left, 2 units up, reflected across the x-axis

Multiple Choice

Identify the Transformations. 

• Vertical stretch by 2 and down 4
• Horizontal compression by ½ and down 4
• Vertical stretch by 2 and up 4
• Horizontal compression by ½ and right 4

Multiple Choice

Describe the transformations.

• Translate Right 2, Down 4
• Translate Left 2, Down 4
• Translate Left 2, Up 4
• Translate Right 2, Up 4

Multiple Choice

Describe the transformation
y = 2√x

• Vertical Compression by 2
• Vertical Expansion by 2
• Vertical Compression by 1/2
• Horizontal Expansion by 2

Multiple Choice

What is the equation of the function that is graphed?

• f(x)= - √x
• f(x) = √-x
• f(x) = - √-x

Multiple Choice

Which is the graph of the square root parent function?

• A
• B
• C
• D

Multiple Choice

What are the transformations to the graph compared to the parent function?

• Shifted right 2, shifted up 3, and reflected over the y-axis
• Shifted left 2, shifted up 3, and reflected over the y-axis
• Shifted left 2, shifted up 3, and reflected over the x-axis
• Shifted right 2, shifted up 3, and reflected over the x-axis

Multiple Choice

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

• Shifted right 5, shifted down 2, and reflected over the x-axis
• Reflected over the x-axis, vertical stretch, and shifted right 5
• Reflected over the x-axis, vertical stretch, and shifted left 5
• Shifted right 5, shifted down 2

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

Domain and Range

Multiple Choice

What is the range of the function in this graph?

• (-infinity, 3]
• [3, infinity)
• (-inifnity, 0]
• [0 infinity)

Multiple Choice

What is the domain of the function in this graph?

• (-infinity, 3]
• [3, inifinity)
• (-infinity, 0]
• [0, infinity)

Multiple Choice

What is the DOMAIN of the function?

• [-3, infinity)
•  [0, infinity)
• [3, inifinity)
• (-infinity, 0}

Multiple Choice

Find the domain and range of the function
Hint:  Use a scratch graph to help you visualize things. 

• Domain: (-∞, ∞)  Range: [-∞, 4]
• Domain: [1, ∞)  Range: (-∞, 4]
• Domain: [-1. ∞) Range: [4, ∞) 
• Domain: [4, ∞) Range: [-1,∞) 

Multiple Choice

Identify the Range

• (- ∞, -2 ]

• [ -2, ∞ )

• All Real Numbers

• [ 0, ∞)

Rational Exponents

Multiple Choice

Write the following expression in exponential form:

• a.)
• b.)
• c.)
• d.)

Multiple Choice

Write the following expression in radical form:

• a.)
• b.)
• c.)
• d.)

Multiple Choice

Write the following expression in exponential form:

• a.)
• b.)
• c.)
• d.)

Multiple Choice

Write the following expression in radical form:

• a.)
• b.)
• c.)
• d.)

Multiple Choice

Write the following expression in radical form:

• a.)
• b.)
• c.)
• d.)

Solving radical equations

Multiple Choice

2∛(x-50) = -10

• 75

• 175

• -75

• -175

Multiple Choice

Solve:

$$3\sqrt{2x+6}+2=20$$  

• 17

• 21

• 0

• 15

Multiple Choice

Solve:

$$4\left(3x-3\right)^{\frac{2}{3}}=36$$  

• x=10, x=-8

• x=-10, x=8

• x=12, x=-6

• x=-12, x=6

Multiple Choice

Solve:

$$\sqrt{x+6}=x+4$$  
Hint: This is like #3 from your notes (the long one)

• x=-5

• x=-2

• x=2

• x=5