Graphing Exponential Functions Concepts

The video tutorial explains how to graph the equation y = -2^(x+2) by first graphing the parent function y = 2^x. It uses a table of values to plot the base graph and identifies key transformations such as reflection over the x-axis and translation to the left. The tutorial guides students through applying these transformations to finalize the graph.

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

• Graph y = 2^x

• Graph y = 2^(x+2)

• Graph y = -2^(x)

• Graph y = -2^x

What is the purpose of using a table of values when graphing y = 2^x?

• To find the slope of the graph

• To identify the y-intercept

• To determine the x-intercept

• To plot key points on the graph

Where does the parent graph y = 2^x always cross the y-axis?

• At (1, 1)

• At (0, 0)

• At (1, 0)

• At (0, 1)

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

• A shift upwards

• A reflection over the x-axis

• A reflection over the y-axis

• A shift to the right

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

• Invert the y-coordinate

• Subtract 1 from both coordinates

• Invert the x-coordinate

• Add 1 to both coordinates

What happens to the point (1, 2) when it is reflected over the x-axis?

• (-1, -2)

• (-1, 2)

• (2, 1)

• (1, -2)

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

• A shift 2 units to the right

• A shift 2 units to the left

• A shift 2 units up

• A shift 2 units down

How do you shift a graph 2 units to the left?

• Add 2 to the y-coordinates

• Add 2 to the x-coordinates

• Subtract 2 from the x-coordinates

• Subtract 2 from the y-coordinates

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

• Reflect over the y-axis

• Reflect over the x-axis

• Shift 2 units to the right

• Shift 2 units to the left

What is the result of applying all transformations to the parent graph y = 2^x?

• A graph shifted down and reflected

• A graph shifted up and reflected

• A graph shifted left and reflected

• A graph shifted right and reflected