Understanding Exponential Functions Concepts

The video tutorial explains how to identify exponential growth and decay in functions, focusing on the role of the base (B) and the initial value (A) as the y-intercept. It provides examples to illustrate these concepts, including a tricky case involving a negative exponent. The tutorial emphasizes the importance of recognizing implicit initial values and offers tips for correctly identifying growth, decay, and y-intercepts in exponential functions.

What is the y-intercept of an exponential function?

• The point where the graph crosses the x-axis

• The slope of the graph

• The initial value of the function

• The highest point on the graph

What does the initial value represent in an exponential function?

• The slope of the graph

• The point where the graph crosses the x-axis

• The starting value of the function

• The highest point on the graph

What happens to the graph of an exponential function when the base is greater than 1?

• The graph becomes a parabola

• The graph represents exponential growth

• The graph becomes a straight line

• The graph represents exponential decay

What happens to the graph of an exponential function when the base is between 0 and 1?

• The graph becomes a parabola

• The graph becomes a straight line

• The graph represents exponential decay

• The graph represents exponential growth

In the function y = 2 * 3^x, what does the base 3 indicate?

• The function represents exponential decay

• The function is quadratic

• The function is linear

• The function represents exponential growth

For the function y = 2 * 3^x, what is the y-intercept?

• 3

• 2

• 1

• 0

What is the base in the function y = 2 * 3^x?

• 1/2

• 2

• 3

• x

In the function y = 2 * 3^x, what is the role of the coefficient 2?

• It is the base of the exponential function

• It is the slope of the function

• It is the exponent of the function

• It is the initial value or y-intercept

In the function y = 2 * (1/2)^x, what does the base 1/2 indicate?

• The function is linear

• The function is quadratic

• The function represents exponential growth

• The function represents exponential decay

For the function y = 2 * (1/2)^x, what is the y-intercept?

• 1/2

• 2

• 1

• 0