Question 1: For the function y=\frac{3}{x-2}, identify the vertical and horizontal asymptotes.

Answer: Vertical: x=2; Horizontal: y=0

Question 2: Calculate the limit of y=\frac{4}{x+1} as x approaches -1 from the right.

Answer: DNE (infinite)

Question 3: Plot the graph of y=\frac{2}{x} on the grid. Identify the asymptotes.

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

Question 1: Given y=\frac{5}{x-3}, find the points where the graph intersects the x-axis and y-axis.

Answer: x=5; y=0 when x→∞

Question 2: Explain how the asymptotes of y=\frac{1}{x+4} change if the function is shifted 3 units to the right and 2 units up.

Answer: Vertical asymptote shifts to x=-1; Horizontal asymptote shifts to y=2

Question 1: A car's speed (in km/h) is modeled by the function v=d/(t-2), where d is the distance traveled in km and t is time in hours. What does the vertical asymptote at t=2 represent in this context?

Answer: It indicates that the model is undefined at t=2 hours, representing a moment just before the car reaches the destination or a point where the model breaks down.

Question 1: Construct the graph of y=\frac{4}{x-1} + 2. Identify the asymptotes and describe how the graph is shifted from y=\frac{4}{x}.

Answer: Vertical asymptote at x=1; horizontal asymptote at y=2; shifted 1 unit right and 2 units up.

Question 2: A reciprocal function has asymptotes at x=\pm 3. Write a possible equation for this function.

Answer: y=\frac{k}{x-3} or y=\frac{k}{x+3}

Question 1: A student claims that the asymptotes of y=\frac{2}{x-5} are x=5 and y=2. Identify and correct the mistake in this statement.

Answer: Incorrect: y=2 is not an asymptote; horizontal asymptote is y=0.

Question 2: Describe a common mistake students make when sketching reciprocal functions and how to avoid it.

Answer: Incorrectly drawing asymptotes or ignoring the asymptotic behavior; avoid by practicing identifying asymptotes first and sketching accordingly.