Transformations of Exponential Functions

The video tutorial explains how to apply transformations to the exponential function f(x) = 2^x. It covers vertical shifts, horizontal shifts, and reflections across the x-axis and y-axis. Each transformation is explained with reference to notes and graphically verified using Desmos. The tutorial aims to help students understand how to manipulate the exponential function through these transformations.

What is the parent function used in the video tutorial?

• f(x) = x^3

• f(x) = x^2

• f(x) = 2^x

• f(x) = 3^x

What is the result of shifting the function f(x) = 2^x two units down?

• g(x) = 2^(x + 2)

• g(x) = 2^x + 2

• g(x) = 2^x - 2

• g(x) = 2^(x - 2)

Which of the following is a vertical shift of the function f(x) = 2^x?

• g(x) = 2^x + 2

• g(x) = 2^x - 2

• g(x) = 2^(x - 2)

• g(x) = 2^(x + 2)

How do you shift the function f(x) = 2^x two units to the right?

• g(x) = 2^x + 2

• g(x) = 2^x - 2

• g(x) = 2^(x - 2)

• g(x) = 2^(x + 2)

What is the effect of a positive horizontal shift on the function f(x) = 2^x?

• The graph moves left

• The graph moves down

• The graph moves right

• The graph moves up

What transformation occurs when reflecting f(x) = 2^x across the x-axis?

• g(x) = 2^(-x)

• g(x) = -2^x

• g(x) = 2^(x + 2)

• g(x) = 2^(x - 2)

What is the graphical effect of reflecting f(x) = 2^x across the x-axis?

• The graph shifts down

• The graph shifts up

• The graph is inverted horizontally

• The graph is inverted vertically

What happens to the x-coordinates when reflecting a function across the y-axis?

• They become negative

• They remain the same

• They halve

• They double

How is the function f(x) = 2^x transformed when reflected across the y-axis?

• g(x) = 2^(-x)

• g(x) = 2^x

• g(x) = 2^(x + 2)

• g(x) = -2^x

Which tool is used in the video to verify the transformations graphically?

• GraphCalc

• Wolfram Alpha

• Desmos

• GeoGebra