Question 1: Plot the graph of y = 1/x for x values of -4, -2, -1, 1, 2, 4. Label the points.

Answer:

Question 2: Calculate y when x = 3 and x = -3 in the function y = 1/x.

Answer: 1/3, -1/3

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

Answer: x=0 and y=0

Question 4: Construct a graph of y = 1/x for positive x values from 1 to 10. Mark key points.

Answer:

Question 5: Plot the reciprocal of the point (2, y). What is the new point?

Answer: (2, 0.5)

Question 6: A rectangle has length 1/x and width x. For x=2, what are the dimensions? Calculate the area.

Answer: Length = 0.5, Width = 2, Area = 1

Question 7: Explain why the graph of y = 1/x has two branches, and describe where each is located.

Answer: One branch in Quadrant I (x>0,y>0), the other in Quadrant III (x<0,y<0).

Question 8: What is the value of y when x approaches 0 from the positive side? What about from the negative side?

Answer: Approaches infinity from the positive side, negative infinity from the negative side.

Question 9: Given the graph y=1/x, find the value of x when y=4 and y = -0.25.

Answer: x=0.25, x=-4

Question 10: Identify a common mistake students might make when plotting y=1/x, and explain how to avoid it.

Answer: Mistake: plotting y-values as if y=1+x or similar. To avoid, remember y=1/x is reciprocal of x.

Question 11: Challenge: For x > 0, find the value of x such that the sum of y=1/x and y=2x equals 2. Show your working.

Answer: x = 0.5