Transformations of Logarithmic Functions

The video tutorial guides viewers through a Khan Academy exercise involving graph transformations. It starts with the graph of y = log base 2 of x and demonstrates how to transform it into y = 4 * log base 2 of (x + 6) - 7. The process involves shifting the graph, scaling it, and making final adjustments to achieve the target equation. The tutorial emphasizes understanding each transformation step and encourages viewers to practice these concepts.

What is the initial graph shown in the exercise?

• y = 2 * log base 2 of x

• y = log base 10 of x

• y = 4 * log base 2 of x

• y = log base 2 of x

What is the target equation for the graph adjustment?

• y = 4 * log base 2 of (x + 6) - 7

• y = log base 2 of (x + 6) - 7

• y = log base 2 of x + 6

• y = 4 * log base 2 of x - 7

What is the effect of replacing x with (x + 6) in the function?

• Shifts the graph 6 units down

• Shifts the graph 6 units up

• Shifts the graph 6 units to the left

• Shifts the graph 6 units to the right

What is the new position of the vertical asymptote after the first transformation?

• x = 0

• x = -6

• x = 6

• x = -12

After the first transformation, where does the point (1, 0) move?

• (-5, 0)

• (7, 0)

• (-1, 0)

• (1, 0)

What happens to the graph when it is multiplied by 4?

• It scales vertically by a factor of 4

• It scales horizontally by a factor of 4

• It shifts 4 units to the right

• It shifts 4 units to the left

What is the y-value of the point when x = -4 after the second transformation?

• 1

• 2

• 4

• 0

What is the final transformation applied to the graph?

• Shift 7 units to the left

• Shift 7 units up

• Shift 7 units to the right

• Shift 7 units down

How does the y-value change when subtracting 7 in the final transformation?

• Remains the same

• Doubles

• Decreases by 7

• Increases by 7

What is the final y-value of the point initially at y = 0 after all transformations?

• 0

• -7

• -14

• 7