Question 1: Calculate the value of y when x = 2 in the equation y = 1/x.

Answer: 0.5

Question 2: Plot the graph of y = 1/x for x values from -3 to 3 (excluding x=0).

Answer: Students will plot points at (-3, -1/3), (-2, -1/2), (-1, -1), (1, 1), (2, 1/2), (3, 1/3).

Question 3: Identify the vertical and horizontal asymptotes of the graph of y = 1/x.

Answer: Vertical asymptote: x=0; Horizontal asymptote: y=0

Question 4: Explain why y = 1/x cannot be graphed at x=0.

Answer: Because division by zero is undefined, y=1/0 does not exist, creating a vertical asymptote at x=0.

Question 5: Calculate the value of y when x = -4 in the equation y = 1/x.

Answer: -0.25

Question 6: Plot the point corresponding to y = 1/x when x = -1/2 on the grid.

Answer: Point at (-1/2, -2)

Question 7: Describe the general shape of the graph of y = 1/x.

Answer: The graph consists of two hyperbolic branches in quadrants I and III and quadrants II and IV, approaching asymptotes.

Question 8: A car is traveling such that its speed is proportional to 1/x, where x is the distance from a starting point. If at x=2, the speed is 0.5 units, find the speed when x=4.

Answer: 0.25 units

Question 9: Construct a triangle on the grid with one vertex at (1,1) and a side length of 3 units, and describe how the reciprocal function could relate to the distances involved.

Answer: Students will draw the triangle; the reciprocal function relates to the inverse of side lengths or gradients.

Question 10: Identify the common mistake students make when plotting y=1/x and how to correct it.

Answer: Mistake: plotting at x=0 or misplacing points in the wrong quadrants. Correction: Remember that y=1/x is undefined at x=0 and ensure points are placed correctly in quadrants I and III or II and IV.

Question 11: Determine whether the point (2, 0.5) lies on the graph of y=1/x. Justify your answer.

Answer: Yes, because 1/2 = 0.5.

Question 12: Challenge: Find the equation of a hyperbola that is a reflection of y = 1/x over the x-axis.

Answer: y = -1/x