Function Transformations and Properties

This video tutorial covers basic functions, including identity, quadratic, absolute value, square root, cubic, rational, exponential, and logarithmic functions. It explains their domains and ranges, and explores how transformations affect these properties. The video uses graphing technology to illustrate these concepts, emphasizing the importance of understanding transformations both inside and outside functions.

What is the primary focus of the video tutorial?

• Advanced calculus techniques

• Statistics and probability

• Basic functions and their transformations

• Trigonometric identities

What is the domain of the identity function y = x?

• 0 to 1

• Negative infinity to infinity

• 0 to infinity

• Negative infinity to 0

How is the range of the quadratic function y = x^2 expressed?

• 1 to infinity

• 0 to infinity

• Negative infinity to infinity

• Negative infinity to 0

What shape does the graph of the absolute value function resemble?

• A U-shape

• A V-shape

• A straight line

• An S-curve

What is the domain of the square root function y = √x?

• Negative infinity to 0

• Negative infinity to infinity

• 1 to infinity

• 0 to infinity

What is the characteristic shape of the cubic function y = x^3?

• An S-curve

• A straight line

• A U-shape

• A V-shape

What is the domain of the hyperbola y = 1/x?

• All real numbers except x = 0

• Negative infinity to infinity

• 0 to infinity

• Negative infinity to 0

What is the horizontal asymptote of the exponential function y = e^x?

• y = 1

• x = 1

• y = 0

• x = 0

What is the domain of the natural logarithm function y = ln(x)?

• 0 to infinity

• Negative infinity to infinity

• 1 to infinity

• Negative infinity to 0

What happens to a graph when a constant is added outside the function?

• It reflects over the x-axis

• It shifts horizontally

• It shifts vertically

• It compresses vertically