Exponential Functions and Their Properties

The video tutorial covers graphing exponential functions, focusing on exponential growth and decay. It explains the components of exponential equations, such as initial value, shifts, and asymptotes. The tutorial demonstrates how to graph exponential growth by shifting and scaling, and introduces exponential decay with reflections. The domain and range of these functions are discussed, along with real-life examples like national debt. The video aims to provide a comprehensive understanding of graphing exponential functions.

What is the initial value in an exponential function?

• The horizontal asymptote

• The value of the base

• The slope of the tangent

• The y-intercept

What does a positive 'a' value indicate in an exponential function?

• Exponential decay

• Exponential growth

• Horizontal shift

• Vertical reflection

How does a left shift affect the graph of an exponential function?

• Moves the graph up

• Moves the graph to the right

• Moves the graph down

• Moves the graph to the left

What is the horizontal asymptote in the first example?

• y = -3

• y = 1

• y = 0

• y = 3

What is the domain of an exponential function?

• Negative infinity to zero

• Zero to one

• Zero to positive infinity

• Negative infinity to positive infinity

In the second example, what does a negative 'a' value cause?

• No change

• Exponential decay

• Vertical reflection

• Horizontal shift

What is the effect of a negative exponent in the second example?

• Increases the base

• Decreases the base

• Reciprocal of the base

• No effect

What is the horizontal asymptote in the second example?

• y = 0

• y = 5

• y = -5

• y = 1

How does the graph behave in the second example after reflection?

• Grows downwards

• Oscillates

• Stays constant

• Grows upwards

What real-life example is given for exponential growth into negatives?

• Radioactive decay

• National debt

• Population growth

• Bacterial growth