Exponential Functions and Transformations

The video tutorial explains transformations of exponential functions, focusing on the parent function f(x) = 2^x. It covers key characteristics such as horizontal asymptotes and the behavior of the function at specific points. The tutorial demonstrates graphing the function and explores various transformations, including vertical and horizontal translations, reflections, and complex transformations. A practice problem is provided to reinforce learning.

What is the parent function used to understand exponential transformations?

• f(x) = 2^x

• f(x) = x^2

• f(x) = e^x

• f(x) = log(x)

Which of the following is a characteristic of an exponential function?

• Horizontal asymptote

• Diagonal asymptote

• No asymptote

• Vertical asymptote

What is the value of 2^0 in the context of the parent function?

• 0

• 1

• 2

• Undefined

How does the graph of f(x) = 2^x change when transformed to f(x) = 2^(x) - 1?

• Shifts right by 1 unit

• Shifts down by 1 unit

• Shifts up by 1 unit

• Shifts left by 1 unit

What happens to the graph of f(x) = 2^x when it is transformed to f(x) = 2^(x-1)?

• Moves 1 unit left

• Moves 1 unit down

• Moves 1 unit up

• Moves 1 unit right

Reflecting the graph of f(x) = 2^x across the x-axis results in which function?

• f(x) = 2^(x+1)

• f(x) = 2^(x-1)

• f(x) = 2^-x

• f(x) = -2^x

What is the effect of the transformation f(x) = -1/2 * 2^(2x-1) + 3 on the parent function?

• Translates 3 units down

• Compresses vertically and horizontally

• Reflects across the y-axis

• Stretches vertically