Reciprocal Graphs and Their Properties

The video tutorial introduces reciprocal graphs, focusing on forms like y = k/x and y = k/x^2. It explains how to sketch these graphs for both positive and negative values of K, emphasizing the importance of asymptotes and the correct approach to drawing lines towards the axes. The tutorial also covers comparing graphs with different K values on the same axis and concludes with practice questions for viewers.

What is the general form of a reciprocal graph?

• y = kx^2

• y = k^2/x

• y = k/x

• y = kx

When k is positive in y = k/x, how does the graph behave?

• It forms a straight line.

• It remains constant.

• It crosses the axes at multiple points.

• It approaches the axes but never touches them.

How does the graph of y = k/x change when k is negative?

• It shifts to the right.

• It reflects across the x-axis.

• It becomes a straight line.

• It remains unchanged.

In the graph of y = k/x^2, what happens when k is negative?

• The graph is a straight line.

• The graph is a circle.

• The graph is below the x-axis.

• The graph is above the x-axis.

What is a key consideration when drawing two graphs on the same axis?

• Ensuring they are both straight lines.

• Ensuring they have the same y-intercept.

• Ensuring they are drawn with different colors for clarity.

• Ensuring they are symmetrical.

How does the graph of y = 5/x differ from y = 3/x?

• y = 5/x is a straight line.

• y = 5/x is further from the axes.

• y = 5/x is closer to the axes.

• y = 5/x is a circle.

What is the shape of the graph for y = -3/x^2?

• Below the x-axis

• Above the x-axis

• A straight line

• A parabola

When drawing y = 5/x^2, what should be noted about its position?

• It is closer to the axes than y = -3/x^2.

• It is further from the axes than y = -3/x^2.

• It is a circle.

• It is a straight line.

What is the importance of ensuring the graph heads towards the axes?

• To ensure it crosses the axes.

• To maintain the correct shape of the graph.

• To make it a straight line.

• To make it a circle.

What should you avoid when sketching reciprocal graphs?

• Using different colors

• Drawing perfect lines

• Adding numbers to the axes

• Drawing multiple graphs