Transformations of Exponential Functions

The video tutorial explains how to graph the equation y = -2^(x+2) by first plotting the parent graph y = 2^x. It involves using a table of values to plot the base graph, identifying transformations such as reflecting over the x-axis, and applying a horizontal shift by moving the graph 2 units to the left. The tutorial concludes with finalizing the graph and reviewing the steps taken.

What is the first step in graphing the equation y = -2^(x+2)?

• Graph y = 2^x as the parent graph.

• Reflect the graph over the y-axis.

• Add 2 to the y-values.

• Shift the graph 2 units to the right.

What is the base point where the graph of y = 2^x always crosses?

• (0, 0)

• (0, 1)

• (1, 1)

• (1, 0)

How do you find additional points for the graph of y = 2^x?

• By adding 1 to each x-value.

• By multiplying each y-value by 2.

• By raising 2 to the power of each x-value.

• By subtracting 1 from each y-value.

What does the negative sign in y = -2^x indicate?

• A reflection over the y-axis.

• A reflection over the x-axis.

• A vertical stretch.

• A horizontal shift.

How do you reflect a point over the x-axis?

• Subtract 1 from the y-coordinate.

• Add 1 to the x-coordinate.

• Invert the y-coordinate.

• Invert the x-coordinate.

What transformation is applied due to the x+2 term in y = -2^(x+2)?

• Shift 2 units up.

• Shift 2 units to the left.

• Shift 2 units down.

• Shift 2 units to the right.

How does the x+2 term affect the graph's position?

• It moves the graph 2 units to the left.

• It moves the graph 2 units down.

• It moves the graph 2 units up.

• It moves the graph 2 units to the right.

What is the final step in graphing y = -2^(x+2)?

• Apply a vertical stretch.

• Combine all transformations and plot the final graph.

• Add 2 to all y-values.

• Reflect the graph over the y-axis.

What should you do after plotting the final graph?

• Erase the parent graph.

• Check for any additional transformations.

• Verify the graph's accuracy.

• Label the axes.

What is the overall effect of the transformations on the graph of y = -2^(x+2)?

• The graph is shifted down and compressed horizontally.

• The graph is shifted up and reflected over the y-axis.

• The graph is shifted left and reflected over the x-axis.

• The graph is shifted right and stretched vertically.