Unit 2 Review- Algebra II Support

Unit 2 Review
Algebra II Support

Multiple Choice

Rewrite log₂8 = 3 in exponential form

• 2⁸ = 3

• 2³ = 8

• 3² = 8

• 8³ = 2

Multiple Choice

Solve for x:
log_x 25 = 2

• 5
• -5
• 1/5
• -1/5

Multiple Choice

Evaluate.
log₃81

• 4
• ¹/₄
• -4
• -¹/₄

Multiple Choice

Condense the expression: log₄6 + log₄3 + log₄v

• log₄2

• log72

• log₄18v

• log₄18

Multiple Choice

Condense the expression: log₄6 + log₄3 + log₄v

• log₄2

• log72

• log₄18v

• log₄18

Multiple Choice

Condense the expression: log₄6 + log₄3 + log₄v

• log₄2

• log72

• log₄18v

• log₄18

Multiple Choice

Condense the expression: log₄6 + log₄3 + log₄v

• log₄2

• log72

• log₄18v

• log₄18

Multiple Choice

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81
• log₈₁3 = 4
• log₃81 = 4
• log₄81 = 3

Match

Match the following:

What is the value of x?

• $$\log_2\left(x\right)=3$$

• $$\log_{25}\left(x\right)=\frac{1}{2}$$

• $$\log_x\left(16\right)=2$$

• $$\log_6\left(\frac{1}{6}\right)=x$$

• $$\log_3\left(1\right)=x$$

8

5

4

-1

0

• 8

• 5

• 4

• -1

• 0

Multiple Choice

Evaluate log ₃₆ 6

• 6

• -6

• 1/2

• Undefined

Multiple Choice

Solve the equation.

• 0

• 2/3

• 3/2

• 1

Multiple Choice

Solve the equation.

• -2

• 0

• 1

• 3

Multiple Choice

log₉(5x + 21) = log₉(2x + 9)

• 9

• -4

• 7

• -10

Multiple Choice

log₇(4x - 5) = log₇(2x + 13)

• 4

• 6

• 9

• -2

Multiple Choice

Which the following graphs shows an exponential decay equation?

Multiple Choice

The asymptote is

• y = 3

• x = 3

• y = 2

• x = 2

Graphing

Graph $$y=2⋅(2)^x−2$$

Multiple Choice

Solve 3³ = 3^{4x + 2}

• x = ¼
• x = -¼
• x = ½
• x = -½

Multiple Choice

Solve for x:
(-3)^x = (-3)¹³

• 13
• -3
• x + 13
• x -13

Hotspot

Select ALL the functions that show an exponential decay.

Multiple Choice

Growth or Decay?

$$f\left(x\right)=\left(\frac{1}{4}\right)^x$$  

• Growth

• Decay

Multiple Choice

Is the pictured graph exponential growth, exponential decay, or linear or none?

• Exponential Growth

• Exponential Decay

• Linear

• None

Multiple Choice

Which graph corresponds to the exponential function $$y=4^x$$  ?

Multiple Choice

Given the function $$y=3\left(2\right)^x$$  , fill in the blank in the table  when  $$x=5$$  .

• 96

• 7776

• 30

• $$-30$$  

Multiple Choice

What is the Inverse of the function $$y=2x+7$$

• $$y=-2x-7$$  

• $$y=7x+2$$  

• $$y=\frac{\left(x-7\right)}{2}$$  

• $$y=\frac{\left(x-2\right)}{7}$$  

Multiple Choice

What is the first step in finding the equation of the inverse of a function?

• get x by itself
• switch x and y
• solve for y
• write the function in inverse function notation

Multiple Choice

What is the inverse of the given coordinates: (1, 2) (3, 8) (-3, 6)

• (1, 2) (3, 8) (-3, 6)
• (1, 2) (8, 3) (-3, 6)
• (-1, -2) (-3, -8) (3, -6)
• (2, 1) (8, 3) (6, -3)

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 the function.

$$f\left(x\right)=5\left(x+6\right)$$

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

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

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

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

Multiple Choice

Find the inverse of $$f\left(x\right)=\frac{1}{2}x-5$$  

• $$f^{-1}(x)=2x+5$$  

• $$f^{-1}(x)=-2x+10$$  

• $$f^{-1}(x)=-2x-5$$  

• $$f^{-1}(x)=2x+10$$  

Finding an output value Example

Math Response

Evaluate the function below at $$f\left(-2\right)$$
$$f\left(x\right)\ =\ -x^{2\ }-\ x\ -\ 1$$

Type answer here

Correct Answer: -3

Deg^°

Rad

Multiple Choice

g(x) = 5 - 6x
Find g(-5)

• g(-5) = -25
• g(-5) = 6
• g(-5) = 4
• g(-5) = 35

Multiple Choice

Given that f(x) = 2x - 2 and g(x) = 5x.  Find the value of f(0) + g(3).

• 13
• 15
• 17
• 0

Multiple Choice

If $$g\left(x\right)=3x^2-5$$  , what is the value of $$g\left(-2\right)$$  ?

• $$-11$$  

• $$-17$$  

• $$7$$  

• $$1$$  

Multiple Choice

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

• 34

• 71

• 35

• 142

Multiple Choice

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

• 2

• 15

• 7

• -9

Multiple Choice

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

• $$4x^2-1$$  

• $$4x^2-2$$  

• $$8x^2-1$$  

• $$16x^2-1$$  

Multiple Choice

If $$f\left(x\right)=\frac{1}{x}$$   and  $$g\left(x\right)=3x+2$$   find $$\left(g\circ f\right)\left(x\right)$$  

• $$\frac{1}{3x}+2$$

• $$3x+2$$  

• $$\frac{3}{x}+2$$  

• $$\frac{1}{3x+2}$$  

Multiple Choice

When $$f(x)=9-3x$$   and $$g(x)=5x-7$$   , find $$\left(f(g(x)\right)$$  

• $$14x-10$$  

• $$-8x+2$$  

• $$30-15x$$  

• $$2x-2$$  

Multiple Choice

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

• $$-6x^2-17x-12$$  

• $$6x^2+x-12$$  

• $$-6x-5$$  

• $$5x+7$$  

Multiple Choice

What's the notation of the inverse of g(x)?

• f(x)

• f^-1(x)

• y

• g^-1(x)

Multiple Choice

Are the following inverses of each other?

• True
• False