Exploring Domain and Range of Exponential Functions

The video tutorial explains how to find the domain and range of exponential growth and decay functions. It covers the identification of growth and decay based on the base of the exponent, the impact of transformations such as vertical stretching and flipping, and how these affect the graph's asymptote. The tutorial provides examples of both growth and decay functions, illustrating how to determine their domain and range using interval notation.

What type of function is f(x) = -4 * 3^(-x)?

• Linear

• Quadratic

• Exponential Growth

• Exponential Decay

What does the number 3 in the function f(x) = -4 * 3^(-x) indicate?

• It is a decay factor.

• It is a growth factor.

• It is a horizontal shift.

• It is a vertical shift.

What is the effect of the negative sign in front of the 4 in f(x) = -4 * 3^(-x)?

• It shifts the graph horizontally.

• It flips the graph across the x-axis.

• It flips the graph across the y-axis.

• It stretches the graph horizontally.

What is the domain of the function f(x) = -4 * 3^(-x)?

• 0 to infinity

• Negative infinity to 0

• Negative infinity to positive infinity

• 0 to 1

In the function f(x) = 7 * (0.75)^x - 5, what does the -5 represent?

• A vertical stretch

• A horizontal shift

• A vertical shift downward

• A horizontal stretch

What is the horizontal asymptote of the function f(x) = 7 * (0.75)^x - 5?

• y = 0

• y = 5

• y = -5

• y = 7

What type of function is f(x) = (15/7) * (4/5)^x + 6?

• Linear

• Exponential Decay

• Exponential Growth

• Quadratic

What is the effect of the +6 in the function f(x) = (15/7) * (4/5)^x + 6?

• It shifts the graph up by 6 units.

• It shifts the graph down by 6 units.

• It stretches the graph vertically.

• It compresses the graph horizontally.

What is the domain of the function f(x) = -5 * 5^x?

• 0 to 1

• 0 to infinity

• Negative infinity to 0

• Negative infinity to positive infinity

What is the range of the function f(x) = -5 * 5^x?

• Negative infinity to 0

• 0 to infinity

• Negative infinity to positive infinity

• 0 to 1