Question 1: Calculate the value of y when x = 4 for the function y = 1/x.

Answer: 0.25

Question 2: Calculate the value of x when y = 0.5 for y = 1/x.

Answer: 2

Question 3: Plot the point corresponding to x=2 on the grid for the graph y=1/x.

Answer: x=2, y=0.5

Question 1: Determine the value of y when x = -3 in y = 1/x.

Answer: -0.333...

Question 2: Construct a graph of y=1/x for x in the range -5 to 5, excluding x=0.

Answer: Plot points at (±1, ±1), (±2, ±0.5), (±3, ±0.333), (±4, ±0.25), (±5, ±0.2)

Question 3: If y=1/x, what is the reciprocal of y when x=2?

Answer: x=1/y=2

Question 4: Explain why the graph of y=1/x has two separate branches, one in each quadrant.

Answer: Because y=1/x is undefined at x=0 and y approaches infinity as x approaches zero from positive and negative sides, creating two separate branches in quadrants I and III, and II and IV.

Question 1: A car travels at a speed inversely proportional to the time taken to reach a destination. If the car takes 4 hours to reach the destination, how long will it take if the speed is doubled?

Answer: 2 hours

Question 2: A worker's productivity is inversely proportional to the hours they work per day. If working 8 hours yields 40 units of output, how many units of output does the worker produce in 10 hours?

Answer: 32 units

Question 3: A water tank fills at a rate inversely proportional to the volume of water already in the tank. If the rate is 2 liters per minute when the tank contains 10 liters, what is the rate when the tank contains 20 liters?

Answer: 1 liter per minute

Question 1: Derive the asymptotes of the graph y=1/x and explain their significance.

Answer: The vertical asymptote at x=0 and horizontal asymptote at y=0. These lines indicate where the graph approaches but never touches the axes, showing the domain and range restrictions.

Question 2: If a function f(x) = k/x passes through the point (3, 2), find the value of k and sketch the graph.

Answer: k=6

Question 1: A student mistakenly plots y=1/x but labels the y-intercept as (0,1). Explain the mistake and correct the interpretation.

Answer: The point (0,1) is undefined because at x=0, y=1/x is undefined. The y-intercept does not exist for y=1/x.

Question 2: Identify and correct the mistake: A student states that y=1/x passes through (2, 0.5) and (4, 0.25) and then claims the graph is a straight line.

Answer: The graph is not a straight line; it is a hyperbola. The points confirm the reciprocal relationship, not linear.