Graph Reflections and Asymptotes

This video tutorial explains how to graph the reflections of the basic rational function f(x) = 1/x. It covers reflections across both the y-axis and x-axis, detailing how changing the sign of the x-values or y-values affects the graph. The tutorial uses key points to demonstrate these reflections and compares the resulting graphs, showing that both reflections result in the same graph for this function.

What is the basic rational function discussed in the lesson?

• f(x) = x + 1

• f(x) = 1/x

• f(x) = x^3

• f(x) = x^2

What happens to the graph of f(x) when the sign of the x-values is changed?

• It reflects across the x-axis

• It shifts downwards

• It shifts upwards

• It reflects across the y-axis

How do you reflect a graph across the y-axis?

• Subtract 1 from all x-values

• Change the sign of the x-values

• Change the sign of the y-values

• Add 1 to all y-values

What is the effect of changing the sign of the x-coordinates on the graph?

• It shifts the graph downwards

• It shifts the graph upwards

• It reflects the graph across the y-axis

• It reflects the graph across the x-axis

What remains unchanged when reflecting the graph across the y-axis?

• The horizontal asymptote

• The y-coordinates

• The x-coordinates

• The vertical asymptote

Which axis is involved when reflecting the graph by changing the sign of the y-values?

• w-axis

• x-axis

• z-axis

• y-axis

What is the result of reflecting the graph of f(x) across the x-axis?

• The graph reflects across the y-axis

• The graph shifts to the left

• The graph shifts to the right

• The graph reflects across the x-axis

What is the effect of changing the sign of the y-coordinates on the graph?

• It shifts the graph to the left

• It reflects the graph across the x-axis

• It reflects the graph across the y-axis

• It shifts the graph to the right

What remains unchanged when reflecting the graph across the x-axis?

• The horizontal asymptote

• The vertical asymptote

• The y-coordinates

• The x-coordinates

What is verified using graphing software in the lesson?

• The graph changes color

• Both reflections result in the same graph

• The graph shifts downwards

• The graph shifts upwards