Logarithmic Functions and Transformations

The video tutorial explains how to write an equation for a transformed logarithm that passes through specific points. It covers the effects of parameters a, b, c, and d on the graph of a common logarithm function. The tutorial demonstrates how to determine these parameter values using given points and substitution. Finally, it simplifies the equation using the change of base formula, providing a clear understanding of the transformation process.

What is the initial form of the equation used to find the transformed logarithm?

• y = a * common log of (B * X) + C + D

• y = a * common log of (X + B) + C + D

• y = a * common log of (B + X) + C + D

• y = a * common log of (B * (X + C)) + D

How does changing the value of 'a' from positive to negative affect the graph?

• It shifts the graph upwards.

• It shifts the graph to the right.

• It causes a vertical reflection.

• It causes a horizontal reflection.

What happens to the graph when 'B' is negative?

• The graph reflects horizontally.

• The graph shifts downwards.

• The graph shifts upwards.

• The graph reflects vertically.

If the vertical asymptote is x = 2, what is the value of 'c'?

• c = 1

• c = 0

• c = 2

• c = -2

What is the simplified form of the equation after determining 'c' and 'b'?

• y = a * common log of (2 + x) + D

• y = a * common log of (2 - x) + D

• y = a * common log of (x - 2) + D

• y = a * common log of (x + 2) + D

What is the value of 'D' after substituting the point (1, 0)?

• D = 1

• D = -1

• D = 2

• D = 0

What is the common log of 1?

• 1

• 0

• 10

• Undefined

After substituting the point (-2, 3), what is the value of 'a'?

• a = 3 / common log 4

• a = 3 * common log 4

• a = common log 4 / 3

• a = 3

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

• y = 3 * log base 4 of (2 - x)

• y = 3 * log base 4 of (x + 2)

• y = 3 * log base 4 of (2 + x)

• y = 3 * log base 4 of (x - 2)

What mathematical concept is used to simplify the equation to log base 4?

• Pythagorean Theorem

• Quadratic Formula

• Binomial Theorem

• Change of Base Formula