Graphing Basic Exponential Functions

The video tutorial explains the graph of exponential functions, highlighting the difference between growth and decay. It covers the basic form y = b^x, where the y-intercept is typically (0,1), and discusses how transformations affect the anchor point. The tutorial provides examples of graphing exponential functions, including those with negative bases and bases less than one, and explains the concept of horizontal asymptotes. It concludes with a discussion on graph transformations and reflections.

What is an exponential function characterized by?

• A constant base

• A variable in the exponent

• A constant as the exponent

• A variable in the base

What does the graph of a basic exponential function resemble?

• A descending airplane

• A car accelerating on a track

• An ascending airplane

• A bird in flight

What is the y-intercept of the graph of the function y = b^x?

• (0, 1)

• (1, 1)

• (1, 0)

• (0, 0)

What does the anchor point (0,1) signify in the graph of y = b^x?

• The lowest point of the graph

• The x-intercept

• The y-intercept

• The highest point of the graph

How does the graph of an exponential function with a larger base grow?

• At a quicker rate

• At a slower rate

• It does not grow

• At the same rate

What happens to the graph of the function y = -b^x?

• It flips over the x-axis

• It flips over the y-axis

• It remains unchanged

• It becomes linear

What is the reciprocal of 1/2?

• 1/2

• 2

• 1/4

• 4

What is the behavior of the graph as x increases for y = (1/2)^x?

• No change

• Linear growth

• Exponential growth

• Exponential decay

What effect does a negative exponent have on the graph of an exponential function?

• It creates a horizontal shift

• It creates a vertical shift

• It inverts the graph across the x-axis

• It inverts the graph across the y-axis

What is the horizontal asymptote for basic exponential functions?

• y = 1

• y = -1

• x = 0

• y = 0