Transform Log Functions

log(4x)

• log4-logx

• log4+logx

• 4logx

• xlog4

log(3x)²

• 2log(3+x)

• 2log3+logx

• log3+2logx

• 2(log3+logx)

• left 3, right 1

• right 3, down 1

• right 3, up 1

• left 3, down 1

How has the graph transformed?

Red is parent graph

Blue is transformation

• left 1 up 6

• left 2 up 4

• left 2 up 6

• up 6

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

Which graph matches the function

*remember the transformation has shifted it right 3 and down 3

• 
• 
• 
• 

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

Describe the transformations of f(x)= -log₂(x+1)

• left 1

• left one & reflected over the y-axis

• left one & reflected over the x-axis

• right one & reflected over the x axis

• ln2+2lnx+lny+4lnz

• ln2+2lnx+lny-4lnz

• 2ln(2xy)-4lnz

• 2ln2x+lny-4lnz