Understanding Graph Transformations

The video tutorial explains the transformation of the graph of y = 2^x. It highlights the reflection across the horizontal axis and a vertical shift. The horizontal asymptote changes from y = 0 to y = 2, indicating a shift up by two units. The equation of the transformed graph is derived as y = -3 * 2^x + 2 by finding the constant 'a' using specific points on the graph. The equation is verified with another point to ensure accuracy.

What transformation is applied to the graph of y = 2^x in the introduction?

• Reflection across the horizontal axis

• Shift downwards

• Shift to the left

• Reflection across the vertical axis

What is the new horizontal asymptote of the transformed graph?

• y = 0

• y = 1

• y = -1

• y = 2

How many units is the graph shifted vertically?

• 1 unit down

• 2 units down

• 2 units up

• 1 unit up

What is the value of 'a' in the equation y = a * 2^x + 2?

• -2

• 3

• 2

• -3

Which point is used to derive the value of 'a'?

• (1, 1)

• (0, -1)

• (0, 1)

• (1, -4)

What is the equation of the transformed graph?

• y = -3 * 2^x + 2

• y = 2 * 2^x - 3

• y = 3 * 2^x + 2

• y = -2 * 2^x + 3

Which point is used to verify the derived equation?

• (1, -4)

• (0, -1)

• (1, 1)

• (0, 1)

What is the result of substituting x = 1 in the derived equation?

• -2

• -3

• -5

• -4

What operation confirms the correctness of the equation?

• Substitution

• Integration

• Differentiation

• Graph plotting

What is the final conclusion about the transformed graph's equation?

• It is incorrect

• It needs further verification

• It is partially correct

• It is verified and correct