Understanding Transformations of Exponential Functions

The video tutorial explains how to transform the graph of f(x) = 2^x to g(x) = -2^x - 1. It covers reflecting the graph across the x-axis and shifting it down by one unit. The tutorial also discusses the domain and range of the transformed graph, using interval notation to describe them. The domain is all real numbers, while the range is y < -1. The video concludes with a summary of the key points covered.

What is the first step in transforming the graph of g(x) from f(x)?

• Add a constant to the function

• Multiply the function by a constant

• Change the base of the exponential function

• Determine the type of reflection

How is the graph of y = 2^x reflected across the x-axis?

• By adding 1 to the exponent

• By changing the base to -2

• By multiplying the function by -1

• By subtracting 1 from the exponent

What happens to the graph when d is changed to -1?

• It becomes a horizontal line

• It shifts down one unit

• It shifts up one unit

• It reflects across the y-axis

What is the domain of the function g(x) after transformation?

• Only integers

• All real numbers

• All negative real numbers

• All positive real numbers

What is the horizontal asymptote of the function g(x)?

• y = 0

• y = -1

• y = 2

• y = 1

What does the domain of a function represent?

• All possible y-values

• The vertical asymptote

• All possible x-values

• The horizontal asymptote

How is the range of g(x) expressed in interval notation?

• (-∞, 0)

• (-∞, -1)

• (-1, ∞)

• (0, ∞)

Why is there a parenthesis to the right of -1 in the range?

• Because -1 is included in the range

• Because -1 is not included in the range

• Because the range is infinite

• Because the range is finite

What does the range of a function represent?

• The horizontal asymptote

• All possible x-values

• The vertical asymptote

• All possible y-values

What is the significance of understanding transformations in functions?

• To solve linear equations

• To graph quadratic functions

• To predict changes in graphs

• To calculate derivatives