Rational Functions Test – Algebra 2 Math (Printable PDF)

Question 1 Domain and asymptotes (2 points)

For f(x) = 4x − 1x + 6, state the domain, the vertical asymptote, and the horizontal asymptote.

Question 2 Transformations (2 points)

Describe the graph of y = –7x − 5 − 2 as a transformation of y = 1x.

Question 3 From graph to equation (3 points)

The graph of y = ax − h + k is shown with the points (0, 2) and (3, −1).

1. Give the equations of both asymptotes. (1 point)
2. Write the equation of the function. (2 points)

Question 4 Hole, asymptotes (3 points)

For f(x) = x² − x − 20x² − 25, find the hole, the vertical asymptote, and the horizontal asymptote.

Question 5 Inverse variation (3 points)

The quantity y varies inversely with x, and y = 8 when x = 7.

1. Determine the constant of variation and write the equation. (1 point)
2. Calculate y at x = 14. (1 point)
3. Determine the value of x that produces y = 2. (1 point)

Question 6 Average cost (3 points)

The average cost per item for a school print shop is A(n) = 5n + 900n dollars when n items are printed.

1. Find the average cost for 150 items. (1 point)
2. Find the number of items for an average cost of $8. (1 point)
3. Identify the horizontal asymptote and explain its meaning in this context. (1 point)

Question 7 Rewrite and identify (2 points)

Rewrite y = 4x − 7x − 3 in the form y = ax − h + k and name both asymptotes.

Question 8 A hole on a graph (2 points)

The figure displays the graph of f(x) = x² − 25x + 5.

1. Name the coordinates of the hole. (1 point)
2. Write the domain in words. (1 point)