Radical to Exponential and Back

Presentation

•

Mathematics

•

11th Grade

•

Hard

Joseph Anderson

FREE Resource

7 Slides • 31 Questions

Radical Equations Unit Test

Composition of Functions

Multiple Choice

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

-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

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?

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

175

-75

-175

Multiple Choice

Solve:

3\sqrt{2x+6}+2=20

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

Radical Equations Unit Test

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