Graphing Exponential Functions: Key Concepts and Techniques

This video tutorial covers lesson 6.3 part two on exponential functions, focusing on graphing them. It explains how to fill out tables with different exponents, plot points, and understand the behavior of graphs with negative exponents. The tutorial also discusses horizontal asymptotes and how different values of B affect the graph's shape, including exponential growth and decay. Additionally, it covers the general form of exponential functions and how shifts in the graph occur due to changes in parameters.

What type of function are we studying in this lesson?

• Quadratic functions

• Linear functions

• Logarithmic functions

• Exponential functions

What happens to exponential functions with negative exponents?

• They remain unchanged

• They result in negative values

• They result in zero

• They result in fractions

How do you plot points for an exponential function on a graph?

• Using only whole numbers

• Using only positive exponents

• Using both positive and negative exponents

• Ignoring negative exponents

What is the shape of the graph when plotting exponential functions?

• Straight line

• Zigzag pattern

• U-shaped curve

• Curved line approaching the x-axis

What does a negative base in an exponential function affect?

• There is no effect

• The graph becomes linear

• The values become non-real

• The graph may reflect over the x-axis

What is the domain of an exponential function?

• All negative numbers

• All positive numbers

• All real numbers

• Only integers

What is the range of an exponential function when the base is greater than 1?

• y is any real number

• y is equal to 0

• y is less than 0

• y is greater than 0

What is a horizontal asymptote in the context of exponential functions?

• A vertical line the graph approaches

• The lowest point of the graph

• A horizontal line the graph approaches but never touches

• The highest point of the graph

How does the graph of an exponential function behave when the base is less than 1 but greater than 0?

• It shows exponential decay

• It remains constant

• It shows exponential growth

• It becomes undefined

What does the parameter 'a' in the general form of an exponential function affect?

• The shift left or right on the graph

• The shift up or down on the graph

• The x-intercept of the graph

• The curvature of the graph