Exponential Functions and Transformations

The video tutorial covers graphing the exponential function y = 12^x. It begins with an introduction to the function and proceeds to create a table of values for graphing. The domain, range, and end behavior of the function are discussed, followed by an exploration of symmetry and the inverse function. Transformations, including horizontal and vertical shifts, are applied to the function. The tutorial concludes with a brief preview of the next topic.

What is the base of the exponential function being graphed?

• 10

• 12

• e

• 2

What is the first step in graphing the function y = 12^x?

• Find the inverse

• Determine the symmetry

• Analyze the end behavior

• Create a table of values

What is the value of y when x = 0 for the function y = 12^x?

• Undefined

• 12

• 1

• 0

What is the domain of the function y = 12^x?

• x > 0

• x < 0

• All real numbers

• x = 0

What is the range of the function y = 12^x?

• All real numbers

• y = 0

• y < 0

• y > 0

What is the horizontal asymptote of the function y = 12^x?

• y = x

• y = 0

• y = 1

• y = 12

In which quadrants is the function y = 12^x positive?

• None

• Quadrant III and IV

• Quadrant I and II

• All quadrants

What happens to y as x approaches negative infinity in the function y = 12^x?

• y becomes negative

• y remains constant

• y approaches infinity

• y approaches 0

Does the function y = 12^x have any symmetry?

• Yes, about the origin

• Yes, about the y-axis

• No symmetry

• Yes, about the x-axis

What is the inverse of the function y = 12^x?

• y = x^12

• y = log_12(x)

• y = 12^(-x)

• y = e^x