Graphing the reciprocal function with multiple transformations

The video tutorial covers the transformation of functions, focusing on graphing techniques, including vertical stretching and shifting. It explains how to find X and Y intercepts algebraically and discusses the domain and range of functions, particularly in relation to asymptotes. The tutorial also touches on the real-world applications of these mathematical concepts, emphasizing the importance of understanding transformations across different types of functions.

What is the effect of the '3' in the equation y = 3 / (x - 1) + 2?

• Horizontal compression

• Vertical stretch

• Horizontal shift

• Reflection

How does subtracting 1 inside the function y = 3 / (x - 1) + 2 affect the graph?

• Stretches the graph vertically

• Reflects the graph over the x-axis

• Shifts the graph right by one unit

• Shifts the graph left by one unit

What is the role of asymptotes in graphing rational functions?

• They are points where the graph crosses the axes

• They indicate where the graph is undefined

• They determine the x-intercepts

• They are the maximum points of the graph

How do you find the y-intercept of the function y = 3 / (x - 1) + 2?

• Find where the graph crosses the x-axis

• Find where the graph crosses the y-axis

• Set y = 0 and solve for x

• Set x = 0 and solve for y

What is the x-intercept of the function y = 3 / (x - 1) + 2?

• x = 2

• x = 0

• x = 1

• x = -1/2

Which x-value is excluded from the domain of y = 3 / (x - 1) + 2?

• x = -1

• x = 2

• x = 1

• x = 0

Why is understanding the domain and range important in function transformations?

• To find the graph's maximum value

• To know where the graph is undefined

• To determine the graph's color

• To identify the graph's shape