Graphing Logarithmic Functions with Transformations

Determine the order of transformations

• left 1, reflected over x-axis
• up 1, reflected over y-axis
• right 1, reflected over x-axis
• left 1, reflected over y-axis

Select all the transformations that apply.

y = log ₆ (x - 1) - 5

• Horizontal shift left 1

• Horizontal shift right 1

• Vertical shift up 5

• Vertical shift down 5

Select all the transformations that apply.

y = log ₅ (x + 1) +1

• Horizontal shift left 1

• Horizontal shift right 1

• Vertical shift up 1

• Vertical shift down 1

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

Select all the transformations that apply.

y = 3log ₃ (2x)

• Vertical stretch by 3

• Vertical shrink by 1/3

• Horizontal shrink by 1/2

• Horizontal stretch by 2

In the general log function 
y = a*log_b(x-h)+k, what letter tells us if the function has moved left or right?

• a
• b
• h
• k

What transformation is occurring vertically? y = 2/3 log x

• stretch

• compression

What transformation is occurring? y = log x - 6

• Horizontal shift left 6

• Horizontal shift right 6

• Vertical shift up 6

• Vertical shift down 6

find the asymptote: y = log₁₀ (x+3)

• x=-3
• x=3
• y=-3
• y=3

Find the asymptote of the following: y = log₁₀ x - 6

• x=6
• x=-6
• x= 0
• y=0