Transformations of Logarithmic Functions

The video tutorial explains how to graph the function y = log base 2 of x and transform it into y = 2 log base 2 of (-x - 3) through a series of transformations. It covers replacing x with -x, shifting the graph by replacing x with x + 3, and finally multiplying the function by 2 to achieve the desired graph.

What is the initial equation given in the problem?

• y = 2 log base 2 of x

• y = log base 10 of x

• y = log base 2 of x

• y = 2 log base 10 of x

What is the first transformation applied to the graph?

• Replace x with x + 3

• Replace x with -x

• Multiply by 2

• Replace x with x - 3

How does replacing x with -x affect the graph?

• Shifts the graph up

• Reflects the graph over the y-axis

• Reflects the graph over the x-axis

• Shifts the graph down

What is the second transformation applied to the graph?

• Replace x with -x

• Replace x with x + 3

• Replace x with x - 3

• Multiply by 2

How does replacing x with x + 3 affect the graph?

• Shifts the graph 3 units to the right

• Shifts the graph 3 units to the left

• Reflects the graph over the y-axis

• Reflects the graph over the x-axis

What is the effect of the transformation on the point where y equals 2?

• It moves to x = -7

• It moves to x = -4

• It moves to x = 4

• It moves to x = 7

What is the final transformation applied to the graph?

• Replace x with x + 3

• Replace x with -x

• Multiply by 2

• Replace x with x - 3

How does multiplying the log expression by 2 affect the graph?

• Shifts the graph up

• Stretches the graph vertically

• Compresses the graph vertically

• Shifts the graph down

What is the final form of the equation after all transformations?

• y = 2 log base 2 of (-x + 3)

• y = log base 2 of (-x + 3)

• y = log base 2 of x

• y = 2 log base 2 of x

What is the final step in sketching the graph?

• Shift 3 units to the left

• Reflect over the x-axis

• Shift 3 units to the right

• Multiply by 2