Exponential Functions and Their Properties

The video tutorial covers graphing the exponential function y = 12^x, including setting up a table of values, plotting the graph, and discussing the domain and range. It explains the end behavior and symmetry of the function, and how to find its inverse. The tutorial also explores transformations, such as horizontal and vertical shifts, and their effects on the graph.

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

• 12

• Undefined

• 1

• 0

Which of the following describes the domain of the function y = 12^x?

• x = 0

• All real numbers

• x < 0

• x > 0

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

• All quadrants

• Quadrant I only

• Quadrant III and IV

• Quadrant I and II

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

• y becomes negative

• y approaches zero

• y remains constant

• y approaches infinity

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

• Symmetric about the y-axis

• Symmetric about the origin

• No symmetry

• Symmetric about the x-axis

How do you find the inverse of the function y = 12^x?

• Subtract 12

• Add 12

• Multiply by 12

• Switch x and y

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

• Linear

• Exponential

• Quadratic

• Logarithmic

What is the effect of a horizontal shift to the right by 2 units on the graph of y = 12^x?

• The graph moves left

• The graph moves down

• The graph moves right

• The graph moves up

If the graph of y = 12^x is shifted down by 3 units, what is the new horizontal asymptote?

• y = -3

• y = 0

• y = 3

• y = 12

What remains unchanged when the graph of y = 12^x is transformed?

• Domain

• Range

• Horizontal asymptote

• Intercepts