Exponential Functions and Their Properties

This tutorial introduces exponential functions, explaining their structure and rules. It provides examples and applications, such as geometric sequences, and discusses patterns in exponential functions. The video also covers graphing techniques, illustrating how exponential functions behave as variables change.

What is the standard form of an exponential function?

• y = a / bx

• y = ax + b

• y = a * bx

• y = a + bx

Why can't the constant A in an exponential function be zero?

• It would make the function linear.

• It would make the function undefined.

• It would make the function equal to zero.

• It would make the function quadratic.

Which of the following is an example of an exponential function?

• y = x^2 + 2

• y = 2 * 7^x

• y = 3x - 1

• y = 2x + 3

How is the population of bacteria modeled in the given example?

• P(x) = 4 + 2x

• P(x) = 2 + 4x

• P(x) = 4 * 2^x

• P(x) = 2 * 4^x

What is the common ratio in an exponential function?

• The sum of the terms

• The difference between terms

• The base of the exponent

• The coefficient of x

How do you determine if ordered pairs represent an exponential function?

• Check if x values increase by multiplication and y values by addition.

• Check if both x and y values increase by multiplication.

• Check if both x and y values increase by addition.

• Check if x values increase by addition and y values by multiplication.

What happens to the graph of an exponential function as x approaches positive infinity?

• The y value approaches zero.

• The y value approaches negative infinity.

• The y value approaches positive infinity.

• The y value remains constant.

What is the effect of a negative constant A on the graph of an exponential function?

• The graph is reflected over the y-axis.

• The graph shifts upwards.

• The graph shifts downwards.

• The graph is reflected over the x-axis.

How does a fractional base affect the graph of an exponential function?

• The graph starts low and ends high.

• The graph starts high and approaches zero.

• The graph remains constant.

• The graph oscillates.