Understanding Graph Transformations

The video tutorial explains how to transform the graph of y=2^x into y=-1*2^(x+3)+4. It covers the steps of shifting the graph to the left by replacing x with x+3, flipping it over the x-axis by multiplying by -1, and finally shifting it up by 4 to adjust the horizontal asymptote. The tutorial concludes by analyzing different graph options to identify the correct transformation.

What is the original function given in the problem?

• y = x + 2

• y = x^2

• y = 2^x

• y = 3^x

What happens to the graph when x is replaced with x + 3?

• It shifts upwards by 3 units.

• It shifts to the right by 3 units.

• It shifts to the left by 3 units.

• It shifts downwards by 3 units.

Which transformation is applied first to the original graph?

• Adding 4

• Multiplying by -1

• None of the above

• Replacing x with x + 3

How does multiplying the function by -1 affect the graph?

• It shifts the graph upwards.

• It shifts the graph downwards.

• It flips the graph over the x-axis.

• It flips the graph over the y-axis.

What is the effect of adding 4 to the function?

• The graph shifts down by 4 units.

• The graph shifts left by 4 units.

• The graph shifts up by 4 units.

• The graph shifts right by 4 units.

What is the new horizontal asymptote after the transformation?

• y = 3

• y = 4

• y = 2

• y = 0

Which choice correctly represents the final transformed graph?

• Choice D

• Choice B

• Choice C

• Choice A

What is the y-value when x = -3 in the final graph?

• 1

• 0

• 3

• 4

What is the y-value when x = -1 in the final graph?

• 0

• 1

• 2

• 3

What is the sequence of transformations applied to the original graph?

• Flip over x-axis, shift left, shift up

• Shift up, shift left, flip over x-axis

• Shift left, flip over x-axis, shift up

• Shift left, shift up, flip over x-axis