Transformations of Logarithmic Functions

The video tutorial explains how to write an equation for a transformed logarithm that passes through specific intercepts. It covers the effects of parameters a, b, c, and d on the graph of a common logarithm, using Desmos for visualization. The tutorial demonstrates how to determine parameter values using given intercepts and simplifies the equation using the change of base formula.

What is the x-intercept of the transformed logarithm equation discussed in the video?

• -2

• -3

• 0

• 2

What is the y-intercept of the transformed logarithm equation?

• -2

• 2

• 0

• -3

Which parameter causes a vertical reflection in the graph of the common logarithm?

• a

• b

• c

• d

Which parameter affects the horizontal reflection of the graph?

• b

• a

• c

• d

What happens to the graph when parameter C is positive?

• Shift right

• Shift up

• Shift down

• Shift left

If the vertical asymptote is at x = -4, what is the value of C?

• 0

• -4

• 4

• -1

What is the effect of a negative value for parameter D?

• Shift up

• Shift left

• Shift right

• Shift down

What is the value of D when the point (-3, 0) is substituted into the equation?

• 0

• -2

• 2

• 1

How is the equation simplified using the change of base formula?

• Using log base 2

• Using log base 4

• Using log base 5

• Using log base 10

What is the final form of the equation using log base 4?

• y = -2 log base 4 of (x + 4)

• y = 2 log base 4 of (x + 4)

• y = -2 log base 10 of (x + 4)

• y = 2 log base 10 of (x + 4)