Transformations of Exponential Functions Explained

The video tutorial covers various transformations applicable to exponential functions, including vertical and horizontal translations, stretching, compressing, and reflections. It provides examples to illustrate these transformations, such as vertical stretching with G(x) = 3 * 2^x and vertical compression and reflection with H(x) = -1/2 * 4^x. Key features like parent functions, intercepts, and asymptotes are identified and explained.

What does a vertical translation of an exponential function involve?

• Reflecting the function over the x-axis

• Adding a constant to the function values

• Stretching the function vertically

• Shifting the function left or right

What effect does replacing x with x - h in a function have?

• Vertical shift

• Vertical stretch

• Horizontal shift

• Horizontal compression

What is the parent function of G(x) = 3 * 2^x?

• 3^x

• 2^x

• 3 * x

• x^2

What type of transformation does G(x) = 3 * 2^x represent?

• Vertical stretch

• Horizontal compression

• Horizontal shift

• Reflection over the y-axis

What is the y-intercept of the function G(x) = 3 * 2^x?

• 3

• 2

• 1

• 0

What transformation is applied in H(x) = -1/2 * 4^x?

• Vertical compression

• Reflection over the x-axis

• Horizontal shift

• Vertical stretch

What is the parent function of H(x) = -1/2 * 4^x?

• -1/2 * x

• 2^x

• 4^x

• x^4

Where is the horizontal asymptote for the function H(x) = -1/2 * 4^x?

• y = 1/2

• y = -1/2

• y = 1

• y = 0

What does the negative sign in H(x) = -1/2 * 4^x indicate?

• Vertical translation

• Horizontal shift

• Vertical stretch

• Reflection over the x-axis

What is the y-intercept of H(x) = -1/2 * 4^x?

• 0

• 1

• -1/2

• -1