Graphing Transformations and Parent Functions

The video tutorial explains how to graph the equation y = -2^(x+2) by first plotting the parent graph y = 2^x. It uses a table of values to plot the parent graph and identifies transformations such as reflection over the x-axis and a horizontal shift to the left. The tutorial concludes with finalizing the graph after applying all transformations.

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

• Reflect the graph over the y-axis.

• Add 2 to the y-values.

• Graph y = 2^x as the parent graph.

• Shift the graph 2 units to the right.

What is a key feature of the parent graph y = 2^x?

• It is a straight line.

• It is a horizontal line.

• It has a maximum point at (0, 1).

• It crosses the y-axis at (0, 1).

What is the purpose of using a table of values in graphing?

• To find specific points on the graph.

• To make the graph a straight line.

• To eliminate the need for transformations.

• To reflect the graph over the x-axis.

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

• Add 1 to the x-values.

• Multiply the y-values by -1.

• Multiply the x-values by -1.

• Subtract 1 from the y-values.

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

• Reflect the graph over the x-axis.

• Reflect the graph over the y-axis.

• Shift the graph downwards.

• Shift the graph upwards.

What transformation is applied due to the x+2 term in the equation?

• Shift the graph 2 units to the right.

• Shift the graph 2 units to the left.

• Shift the graph 2 units down.

• Shift the graph 2 units up.

How do you apply a horizontal shift to a graph?

• Adjust the x-values by the opposite of the number inside the function.

• Adjust the y-values by the number inside the function.

• Multiply the x-values by the number inside the function.

• Multiply the y-values by the number inside the function.

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

• Reflect the graph over the y-axis.

• Combine all transformations and plot the final graph.

• Add 2 to the y-values.

• Shift the graph 2 units up.

What should you do after applying all transformations to the graph?

• Reflect the graph over the y-axis.

• Add more points to the graph.

• Erase the parent graph.

• Check the graph for accuracy.

Why is it important to understand the parent graph before applying transformations?

• It eliminates the need for a table of values.

• It makes the graph a straight line.

• It helps in understanding the basic shape and behavior of the graph.

• It allows you to skip the transformation steps.