Graph Piecewise Functions

The video tutorial covers graphing functions separately, starting with y = 3, a basic algebra topic. It explains transformations, including shifts and asymptotes, and how to graph with constraints. The instructor adjusts graph values to avoid errors and identifies the domain and range of the function.

What is the basic graph of the function y = 3?

• A parabolic curve

• A diagonal line through the origin

• A horizontal line at y = 3

• A vertical line at x = 3

How does the graph of y = 1/X - 2 + 1 shift when the transformation X - 2 is applied?

• 1 unit up

• 1 unit down

• 2 units to the right

• 2 units to the left

What happens to the asymptotes when the graph is shifted 2 units to the right?

• They remain unchanged

• They shift 2 units to the left

• They shift 2 units to the right

• They shift 1 unit up

What is the significance of a 'hole' in the graph?

• It marks the maximum value of the function

• It indicates a point where the function is undefined

• It represents the average value of the function

• It shows where the graph intersects the y-axis

For which value of x is the function y = 1/X - 2 + 1 not defined?

• x = 4

• x = 3

• x = 5

• x = 2

What is the domain of the function y = 1/X - 2 + 1?

• All real numbers

• All real numbers except x = 2

• All real numbers except x = 3

• All real numbers except x = 2 and x = 3

What is the range of the function y = 1/X - 2 + 1?

• All real numbers

• All real numbers except y = 1

• All real numbers except y = 2

• All real numbers except y = 1 and y = 2