Exponential Functions and Graphs

The video tutorial explains how to sketch graphs of exponential equations, focusing on exponential growth and decay. It begins with finding the Y-intercept and understanding the behavior of exponential growth graphs. The tutorial then covers techniques for sketching graphs accurately by testing points. It also introduces exponential decay, explaining how the graph behaves as values change. The video concludes with a summary of graphing techniques for exponential functions.

What is the Y-intercept of the graph for the equation Y = 2 * 2^X?

• 0

• 1

• 2

• 4

How does the graph of Y = 2 * 2^X behave as X becomes very negative?

• It approaches zero but never crosses it

• It becomes negative

• It remains constant

• It oscillates

What is the value of Y when X equals 2 for the equation Y = 2 * 2^X?

• 10

• 4

• 6

• 8

What is the decay factor in the new equation introduced in the video?

• 1/12

• 1/8

• 1/4

• 1/2

What is the initial value of the function with a decay factor of 1/12 when X equals 0?

• 1

• 12

• 3

• 6

How does the graph of an exponential decay function behave as X becomes very positive?

• It increases

• It decreases

• It remains constant

• It oscillates

What is the value of Y when X equals 2 for the decay function introduced?

• 1

• 1.5

• 2

• 2.5

Which of the following best describes an exponential growth graph?

• It oscillates

• It slopes downward

• It remains flat

• It curves upward

Which of the following best describes an exponential decay graph?

• It slopes upward

• It remains flat

• It curves downward

• It oscillates

What is a key step in sketching exponential graphs accurately?

• Using a ruler

• Drawing freehand

• Testing additional points

• Ignoring the Y-intercept