Characteristics of Transformations of Exponential and Logarithmic Functions

The range of logarithmic functions ​ (a)  

• is all real numbers

• is from the vertical asymptote to infinity

• cannot be determined without having the function

What is the asymptote of the exponential function shown?

• y = -7

• y = 7

• y = 4

• y = 6

What is the range of the exponential function shown?

• y > -7

• y < -7

• y > 4

• y > 6

Describe the transformations of the exponential function shown.

• Stretch by a factor of 7, shift left 4, and shift down 7.

• Stretch by a factor of 7, shift right 4, and shift down 7.

• Shrink by a factor of 7, shift left 4, and shift down 7.

• Stretch by a factor of 7, shift left 4, and shift up 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

Describe the transformation on

• The graph has been shifted 3 units up

• The graph has been shifted 3 units to the right

• The graph has been shifted 2 units right

• The graph has been shifted 3 units left

Describe the transformation on

• The graph has been shifted 3 units up

• The graph has been shifted 3 units to the right

• The graph has been shifted 2 units right

• The graph has been shifted 3 units left

Describe the transformations of the exponential function shown.

• Reflection over the x-axis, shift right 5 and shift down 2.

• Shift right 5 and shift down 2.

• Reflection over the x-axis, shift left 5 and shift down 2.

• Shift right 5 and shift up 2.

Describe the transformations of the exponential function shown.

• Shrink by a factor of 2/3 and shift right 10.

• Shrink by a factor of 2/3 and shift left 10.

• Stretch by a factor of 5 and shift left 10.

• Stretch by a factor of 5 and shift right 10.