Interpreting Functions Test – Algebra 2 Math (Printable PDF)

Question 1 Rectangle area model (3 points)

A rectangular pen is built with 30 feet of fencing, so its area is A(w) = w(15 − w) for width w.

1. State a reasonable domain. (1 point)
2. Write A(w) in vertex form. (1 point)
3. State the maximum area and the width that gives it. (1 point)

Question 2 Average rate of change (2 points)

On the stretch from x = 1 to x = 3, how fast does k(x) = x⁴ − 3x change, on average?

Question 3 Rates from a table (2 points)

A drone’s distance traveled is shown in the table.

Find the average speed over each 2-second interval after the start and describe the trend.

Question 4 Zeros by completing the square (2 points)

Complete the square to solve x² − 8x + 7 = 0 and give the vertex of y = x² − 8x + 7.

Question 5 Features of a rational graph (3 points)

The graph shows f(x) = 2/(x − 1) + 3.

1. State the domain. (1 point)
2. Give the vertical asymptote. (1 point)
3. Give the horizontal asymptote. (1 point)

Question 6 Compare a line and an exponential (3 points)

Function A is A(x) = 3x + 10. Function B is given by B(0) = 4, B(1) = 8, B(2) = 16, B(3) = 32.

1. Find the average rate of change of each from 0 to 3. (1 point)
2. Find A(5) and B(5), assuming B keeps doubling. (1 point)
3. Which is larger for large x, and why? (1 point)

Question 7 Trig model features (2 points)

A model is f(t) = 5 sin(πt/4) + 20. Find the period, the maximum value and the minimum value.

Question 8 Value of a device (2 points)

A tablet’s value is V(t) = 1200(0.9)^t dollars after t years. Find the average rate of change from t = 0 to t = 2 and interpret it.

Question 9 Domain of a logarithm (1 point)

State the domain of f(x) = log(x − 4).