Question 1: In reciprocal graphs of y = k/x, vertical asymptotes occur where the denominator is zero, and horizontal asymptotes are at y=0. These asymptotes help define the shape of the graph.

Answer: Vertical asymptote at x=0; horizontal asymptote at y=0

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

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

Question 2: Plot the graph of y=2/x on the grid. Identify the asymptotes.

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

Question 3: Construct the graph of y=1/(x-2). What is the asymptote, and where is it located?

Answer: Vertical asymptote at x=2

Question 4: Identify the asymptotes of y=-4/x+1.

Answer: Vertical: x=0; Horizontal: y=1

Question 5: Explain why y=0 is always a horizontal asymptote for graphs of y=k/x.

Answer: As x approaches infinity or negative infinity, y approaches 0, so y=0 is a horizontal asymptote.

Question 6: The graph of y=5/(x+3) has a vertical asymptote at x=−3. Find its horizontal asymptote.

Answer: y=0

Question 7: Plot y=−1/x on the grid and label the asymptotes. Describe the shape of the graph.

Answer: Vertical asymptote at x=0; Horizontal at y=0; graph in quadrants I and III, approaching asymptotes.

Question 8: Solve for x: y=4/x, when y=2. What is the asymptote involved here?

Answer: x=2; vertical asymptote at x=0

Question 9: A graph of y=k/x intersects the x-axis at x=4 when y=1. Find the value of k and identify the asymptotes.

Answer: k=4; vertical asymptote at x=0; horizontal asymptote at y=0

Question 10: Construct a reciprocal graph with asymptotes at x=−2 and y=3. Write the equation of the graph.

Answer: y=3/(x+2)

Question 11: Identify the errors in this statement: 'The graph of y=2/x has no asymptotes because it is a smooth curve.' Explain and correct the mistake.

Answer: The statement is incorrect; y=2/x has vertical asymptote at x=0 and horizontal asymptote at y=0. The curve approaches but never touches these lines.