Exponential Functions and Transformations

The video tutorial by Anil Kumar covers exponential transformations, focusing on how to describe and perform transformations on functions with a base of 3. It includes detailed explanations of specific transformations, the importance of order in transformations, and how to sketch functions and determine their domain and range. The tutorial also discusses parent functions and provides additional tips for understanding transformations.

What is the main focus of the video tutorial?

• Linear equations

• Quadratic equations

• Exponential equations and transformations

• Trigonometric functions

What is the parent function discussed in the video?

• y = log(x)

• y = x^2

• y = 3^x

• y = 2^x

What are the critical points of the parent function y = 3^x?

• (1, 0) and (3, 1)

• (0, 3) and (1, 9)

• (0, 1) and (1, 3)

• (0, 0) and (1, 1)

What is the domain of the function y = 3^x?

• x belongs to real numbers

• x < 0

• x is an integer

• x > 0

What is the range of the function y = 3^x?

• y belongs to real numbers

• y < 0

• y is an integer

• y > 0

In transformation 1a, what does the negative sign in f(x) = -3^(2x) + 1 indicate?

• Vertical compression

• Horizontal shift

• Reflection on the x-axis

• Vertical stretch

In transformation 1a, what does the '2' in the exponent of f(x) = -3^(2x) + 1 represent?

• Horizontal compression

• Vertical stretch

• Vertical compression

• Horizontal stretch

In transformation 1a, what does the '+1' in f(x) = -3^(2x) + 1 indicate?

• Horizontal shift right

• Horizontal shift left

• Vertical shift down

• Vertical shift up

In transformation 1b, what does the factor (3/4) in g(x) = (3/4) * 3^(-x-1) - 2 indicate?

• Vertical compression

• Horizontal compression

• Vertical stretch

• Horizontal stretch

In transformation 1b, what does the '-x' in the exponent of g(x) = (3/4) * 3^(-x-1) - 2 represent?

• Vertical shift

• Horizontal shift

• Reflection on the y-axis

• Reflection on the x-axis