Logarithmic Transformations

Match the graph with its equation

• y = log₅ (x + 1) + 1 

• y = log₅ (x - 1) + 1 

• y = log₅ (x²) + 1 

• y = log₅ (x)-1

What are the transformations of this graph?

• Right 1 Up 5

• Right 1 Down 5

• Left 1 Up 5

• Left 1 Down 5

Logarithmic functions are the inverse of...

• Linear Functions

• Exponential Functions 

• Quadratic Functions 

• Polynomial Functions 

Select all the transformations that apply.

y = -2 log _1/2 x

• Vertical stretch by 2

• Vertical shrink by 1/2

• Reflection across the y-axis

• Reflection across the x-axis

Use y=log(x) as a parent function. To graph y=log(x-4)+7, the parent function should be translated vertically ​ (a)   (up or down) by ​ ​ (b)   units. The vertical asymptote should be shifted horizontally to the ​ (c)   (left or right) by ​ (d)   units.

• up

• right

• 4

• down

• left

• 7

Write the equation of a natural logarithmic function that has been shifted two units to the left, one unit up, and vertically stretched by a factor of three. (Begin your answer with "y=." Use parentheses where necessary.)

Mathematical Equivalence

ON

Write the equation of a natural logarithmic function that has been shifted two units to the left, one unit up, and vertically stretched by a factor of three.

(Begin your answer with "y=." Use parentheses where necessary.)

Mathematical Equivalence

ON

What is the Range?

• y > 0

• All Real Numbers

• y > 1

• y < 1

What is the equation of the asymptote?

• x = -3

• x=5

• y= -3

• y=5

Describe the graph of f(x) = log x changed to f(x) = 3log(x + 1) - 5

• vertical stretch by 3 and shift right 1 and 5 units down

• vertical stretch by 3 and shift left 1 and 5 units down

• vertical compress by 3 and shift right 1 and 5 units down

• vertical compress by 3 and shift left 1 and 5 units down