Graphing the exponential function with transformations

The video tutorial covers the basics of exponential functions, focusing on growth and decay based on the base value. It explains how the graph behaves when the base is greater than or less than one, and how reflections and shifts affect the graph. The tutorial concludes with an analysis of the final graph and how to identify it among multiple options.

What happens to the graph of an exponential function when the base is greater than one?

• It becomes a horizontal line.

• It remains constant.

• It grows rapidly.

• It shows exponential decay.

Which of the following indicates an exponential decay?

• The base is greater than one.

• The base is less than one.

• The function is multiplied by a positive number.

• The graph shifts upwards.

What effect does multiplying an exponential function by a negative value have?

• It shifts the graph upwards.

• It makes the graph steeper.

• It reflects the graph over the y-axis.

• It shifts the graph to the right.

How does a vertical shift affect the asymptote of an exponential graph?

• The asymptote disappears.

• The asymptote shifts vertically.

• The asymptote shifts horizontally.

• The asymptote remains unchanged.

When visualizing graph transformations, what is a key step in identifying the correct graph?

• Only considering the y-intercept.

• Comparing the graph to multiple options.

• Focusing only on the x-axis.

• Ignoring the asymptote.