Understanding Graph Transformations

The video tutorial explains the graph of the function f(x) = 1/x and its transformations. It covers horizontal and vertical shifts, reflections across the x-axis, and vertical stretches. Each transformation is matched with a corresponding graph, demonstrating how the function changes. The tutorial concludes with a review of basic transformations, including reflections, shifts, and stretches.

What is the basic function discussed in the video?

• f(x) = x + 1

• f(x) = x^2

• f(x) = 1/x

• f(x) = x - 1

Which quadrant does the basic function f(x) = 1/x occupy?

• Third and fourth quadrants

• Second and fourth quadrants

• First and third quadrants

• First and second quadrants

How does the graph of y = 1/(x-3) differ from the basic function?

• It shifts 3 units up.

• It shifts 3 units to the left.

• It shifts 3 units to the right.

• It shifts 3 units down.

What transformation occurs with the function y = 1/x - 3?

• The graph shifts 3 units to the right.

• The graph shifts 3 units to the left.

• The graph shifts 3 units up.

• The graph shifts 3 units down.

What is the effect of subtracting a constant from f(x) in terms of graph transformation?

• Rotation

• Vertical shift

• Horizontal shift

• Reflection

What happens to the graph when using the function y = -1/x?

• It reflects across the y-axis.

• It reflects across the x-axis.

• It shifts up by 1 unit.

• It shifts down by 1 unit.

What is the result of multiplying f(x) by a negative constant?

• Horizontal shift

• Vertical stretch

• Reflection across the y-axis

• Reflection across the x-axis

How does the function y = 3/x transform the graph?

• It compresses the graph vertically.

• It stretches the graph vertically.

• It shifts the graph horizontally.

• It reflects the graph across the y-axis.

What type of transformation is a vertical stretch?

• Adding a constant to the function

• Subtracting a constant from the function

• Multiplying the function by a constant greater than 1

• Dividing the function by a constant

What is the effect of multiplying f(x) by a constant greater than 1?

• Horizontal stretch

• Horizontal compression

• Vertical compression

• Vertical stretch