Exploring Characteristics of Exponential Functions

The video tutorial discusses the characteristics of exponential functions, focusing on domain, range, asymptotes, and end behavior. It uses two examples to illustrate how to determine these characteristics, including whether the function represents growth or decay. The tutorial emphasizes understanding the relationship between the curve and its asymptote to identify growth or decay and explains how to express range as an inequality.

What is the domain of the exponential function in Example 1?

• Negative numbers only

• Positive numbers only

• All real numbers

• Numbers greater than -6

What is the range of the exponential function in Example 1?

• y > 0

• y < -6

• y > -6

• y < 0

Is the graph in Example 1 increasing or decreasing?

• Fluctuating

• Decreasing

• Increasing

• Constant

What type of behavior does the graph in Example 1 exhibit?

• Exponential growth

• Linear decay

• Exponential decay

• Linear growth

As x approaches negative infinity in Example 1, what happens to the graph?

• Approaches positive infinity

• Approaches negative infinity

• Remains constant

• Approaches zero

What is the domain of the exponential function in Example 2?

• All real numbers

• Positive numbers only

• Negative numbers only

• Numbers less than 4

What is the range of the exponential function in Example 2?

• y < 0

• y > 4

• y < 4

• y > 0

Is the graph in Example 2 increasing or decreasing?

• Decreasing

• Increasing

• Constant

• Fluctuating

What type of behavior does the graph in Example 2 exhibit?

• Linear growth

• Exponential growth

• Linear decay

• Exponential decay

As x approaches positive infinity in Example 2, what happens to the graph?

• Approaches negative infinity

• Remains constant

• Approaches positive infinity

• Approaches zero