Exponential Functions and Their Graphs

The video tutorial explains how to match exponential functions with their corresponding graphs. It covers the characteristics of exponential growth and decay, focusing on functions g(x), h(x), k(x), and f(x). The tutorial demonstrates how to identify increasing and decreasing functions and how negative signs affect graph reflections across the x-axis. Graphing software is used to verify the reflections and correct graph matches.

What is the behavior of the function g(x) = 3^x?

• It is a constant function.

• It has negative values.

• It is an increasing function.

• It is a decreasing function.

What is the base of the function g(x) = 3^x?

• 3

• 1

• 1/3

• 0

Which of the following describes the function h(x) = -3^x?

• It is a reflection of g(x) = 3^x across the x-axis.

• It has positive values.

• It is a reflection of g(x) = 3^x across the y-axis.

• It is an increasing function.

What is the effect of the negative sign in h(x) = -3^x?

• It makes the function constant.

• It makes the function values positive.

• It reflects the function across the y-axis.

• It reflects the function across the x-axis.

How does changing the value of 'a' to -1 affect the graph of y = a * 3^x?

• It reflects the graph across the y-axis.

• It shifts the graph upwards.

• It shifts the graph downwards.

• It reflects the graph across the x-axis.

What is the nature of the function k(x) = (1/3)^x?

• It is a constant function.

• It has negative values.

• It is a decreasing function.

• It is an increasing function.

What is the base of the function k(x) = (1/3)^x?

• 1/3

• 0

• 3

• 1

What happens to the graph of k(x) = (1/3)^x when it is reflected across the x-axis?

• It becomes a constant function.

• It becomes an increasing function.

• It becomes f(x) = -(1/3)^x.

• It becomes a linear function.

Which function is a reflection of k(x) = (1/3)^x across the x-axis?

• y = 1

• f(x) = -(1/3)^x

• h(x) = -3^x

• g(x) = 3^x

What is the effect of changing 'a' to -1 in y = a * (1/3)^x?

• It reflects the graph across the x-axis.

• It reflects the graph across the y-axis.

• It shifts the graph downwards.

• It shifts the graph upwards.