Exploring Exponential Function Graphing and Transformations

The video tutorial covers exponential functions, including their definitions, characteristics, and types such as growth and decay. It explains how to graph these functions and describes their transformations, including vertical and horizontal shifts and reflections. Real-life examples, such as cell phone subscriber growth and drug decay, are used to illustrate these concepts.

What defines an exponential function?

• The function is a straight line.

• The variable is in the base.

• The variable is in the exponent.

• The function has a constant base.

What is the form of an exponential growth function?

• f(x) = a to the power of x, where a < 1

• f(x) = a to the power of x, where a = 0

• f(x) = a to the power of -x, where a > 1

• f(x) = a to the power of x, where a > 1

What is the y-intercept of an exponential function?

• (1, 1)

• (0, 1)

• (1, 0)

• (0, 0)

What does a negative exponent in an exponential function indicate?

• Exponential decay

• Quadratic function

• Exponential growth

• Linear function

What is the horizontal asymptote of an exponential decay function?

• y = 1

• y = 0

• x = 0

• x = 1

How does the graph of an exponential function change with a base between 0 and 1?

• It shows exponential growth.

• It remains constant.

• It becomes a straight line.

• It shows exponential decay.

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

• Changes the x-intercept

• Changes the y-intercept

• Changes the slope

• Does not affect the graph

What transformation occurs when you add a positive constant to the exponent?

• Vertical shift up

• Horizontal shift right

• Horizontal shift left

• Vertical shift down

What is the initial value in an exponential decay problem?

• The base of the function

• The decay rate

• The exponent at time zero

• The function's value at time zero

What does the base of an exponential function represent in a growth scenario?

• Decay factor

• Initial value

• Horizontal asymptote

• Growth factor