Question 1: Plot the graph of y = 1/x for x values from -3 to 3, excluding x=0.

Answer: Plot the hyperbola with branches in quadrants I and III, approaching axes asymptotically.

Question 2: Calculate the value of y when x = 2 and x = -4.

Answer: 0.5 and -0.25

Question 3: Identify the key asymptotes of the graph of y = 1/x.

Answer: x=0 and y=0

Question 4: Explain why the graph of y = 1/x never touches the x-axis or y-axis.

Answer: Because y=1/x approaches zero but never equals zero, and x=0 causes undefined y-values.

Question 5: Plot the point (1/2, 2) on the grid and verify if it lies on y = 1/x.

Answer: Yes, because 1/(1/2) = 2.

Question 6: A student plots y=1/x but draws a straight line passing through (1,1) and (-1,-1). Is this correct? Explain.

Answer: No, because y=1/x is a hyperbola, not a straight line.

Question 7: Construct a graph of y = 2/x and compare it to y = 1/x. How are they similar and different?

Answer: Both are hyperbolas with asymptotes at x=0 and y=0; y=2/x is steeper, scaled vertically.

Question 8: Identify a common mistake students make when plotting y=1/x and explain how to correct it.

Answer: Plotting y=1/x as a straight line or only in one quadrant. Correct by plotting points in all quadrants and recognizing the hyperbolic shape.

Question 9: Given the graph of y=1/x, find the value of x when y=4.

Answer: x=1/4

Question 10: A student claims the graph of y=1/x is symmetric about the y-axis. Is this correct? Justify your answer.

Answer: No, because it is symmetric about the origin, not the y-axis.

Question 11: Identify and correct the common mistake: A student plots y=1/x but draws a straight line with endpoints (1,1) and (2, 0.5).

Answer: Mistake: plotting a straight line instead of the hyperbola. Correction: plot multiple points to form the hyperbolic branches.