Exponential and Logarithmic Transformation

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

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

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

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

Using y=3^x as the parent function, what will y=3^-x look like?

• Reflection on the x axis

• Reflection on the line y=x

• Reflection on the y axis

• Reflection on y=0

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

The asymptote of y = log₂(x + 2) will shift...

• right two to x = 2

• left two to x = -2

• not shift and remain x = 0

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

• left one & y-axis reflection

• right one & y-axis reflection

• left one & x-axis reflection

• right one & x-axis reflection

Is this exponential growth or decay?

• Growth

• Decay