Transformations of logarithmic functions

Which graph best represents the following logarithmic function?
 $y=\log_4x$  

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• 
• 
• 

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Which type of function has a horizontal asymptote?

• exponential

• logarithm

• both

• neither

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.7

Which type of function has a vertical asymptote?

• exponential

• logarithm

• both

• neither

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Where is the asymptote?

• x = 1
• y = 1
• x = -1
• y = -1

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

What is the domain?

• $x>1$

• $x<1$

• $y>1$

• $y<1$

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.B.5

What is the range?

• All real numbers

• $x>1$

• $y<2$

• $y>1$
  

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Using the parent function  $y=\log_3x$   what would the graph of  $y=\log_3\left(x+5\right)$   look like?

• Horizontal shift left 5 units

• Horizontal shift right 5 units

• Vertical shift up 5 units

• Vertical shift down 5 units

Tags

CCSS.HSF.BF.B.3

Using the parent function 

 $y=\log_3x$ what would the graph of  $y=\log_3x+5$   look like?

• Horizontal Shift to the right 5 units

• Horizontal shift to the left 5 units

• Vertical shift 5 units up

• Vertical shift 5 units down

Tags

CCSS.HSF.BF.B.3

What is the Vertical Asymptote?

• x = 5

• x = -1

• y = 0

• x = 1

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

What are the transformations of this function?

 $y=\frac{1}{3}\log_2x-8$  

• vertical compression by 1/3, down 8

• vertical stretch by 1/3, down 8

• vertical compression by 1/3, right 8

• reflection across the x-axis, right 8

Tags

CCSS.HSF.BF.B.3