Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Early problems compute one feature. Later ones combine models for revenue, cost, savings and tides.
Standards: F-IF.B.4, F-IF.B.5, F-IF.B.6, F-IF.C.8a, F-IF.C.9 · Level: Grade 11 Algebra 2
Problem 1 Domain in context ★★★
A ball is thrown so that its height in feet is h(t) = −16t2 + 64t, with t in seconds. Find when the ball lands, and state a reasonable domain.
Problem 2 Average rate of change from an equation ★★★
A warehouse robot is s(t) = t3 + 2t feet from its dock after t seconds. Compute (s(4) − s(1)) ÷ (4 − 1) and say what it measures.
Problem 3 Interpret a linear model ★★★
A tank holds V(t) = 640 − 16t gallons after t minutes, for 0 ≤ t ≤ 40. Interpret 640 and −16, and find when 200 gallons remain.
Problem 4 Average rate of change from a table ★★★
The table shows the distance a cyclist has traveled. Find the average speed from 2 to 5 minutes and from 5 to 9 minutes, and tell which is greater.
Problem 5 Average rate of change from a graph ★★★
The graph shows y = √x for x ≥ 0. Use the marked points to find the average rate of change from x = 1 to x = 9.
Problem 6 Complete the square ★★★
Write x2 + 6x + 5 in vertex form and give the vertex.
Problem 7 Zeros, axis and minimum ★★★
For f(x) = x2 − 7x + 10, factor to find the zeros, the axis of symmetry and the minimum value.
Problem 8 Maximum height ★★★
A launched tennis ball has height h(t) = −16t2 + 48t + 6 feet. Rewrite it in vertex form and state the maximum height and when it occurs.
Problem 9 Revenue model ★★★
A shop’s weekly revenue is R(p) = −6p2 + 168p dollars at price p. Find the price that maximizes revenue, the maximum revenue, and the domain in context.
Problem 10 Exponential decay features ★★★
For f(x) = 250(0.8)x, state the y-intercept, the percent decrease per unit, the horizontal asymptote, and the average rate of change from x = 0 to x = 3.
Problem 11 Logarithmic features ★★★
For f(x) = log2(x + 3), find the domain, the vertical asymptote and the x-intercept.
Problem 12 Tide features ★★★
The water depth in feet at a pier is d(t) = 4 sin(πt/6) + 10, where t is hours after midnight. Find the period, the maximum and minimum depths, and the average rate of change from t = 0 to t = 3.
Problem 13 Average cost with an asymptote ★★★
The average cost per item of making x items is C(x) = (500 + 20x)/x dollars. State the domain in context, the horizontal asymptote and its meaning, and C(25).
Problem 14 Features of a cubic ★★★
The graph shows p(x) = x(x − 2)(x − 4). List the zeros, the intervals where p(x) > 0, and the end behavior.
Problem 15 Compare a line and a table ★★★
Function f is given by f(x) = 3x + 8. Function g is given by the table below. Compare their starting values and rates of change, and say which is larger at x = 10.
Problem 16 Compare two quadratics ★★★
Quadratic f(x) = −(x − 2)2 + 7. Quadratic g has the values (0, −2), (1, 2), (2, 4), (3, 4), (4, 2). Which has the greater maximum value, and which has the axis of symmetry farther right?
Problem 17 Population change from a table ★★★
A town’s population was 12,400 in 2010, 13,750 in 2015 and 15,900 in 2020. Find the average rate of change for each five-year period and describe the trend.
Problem 18 Completing the square with a leading coefficient ★★★
Rewrite f(x) = 3x2 − 18x + 10 in vertex form, give the minimum, and find the zeros to the nearest hundredth.
Problem 19 Exponential versus linear savings ★★★
Account A is worth 1,000(1.05)t dollars after t years. Account B is worth 1,200 + 80t dollars. Compare their values at t = 10, 20 and 30, and estimate when A overtakes B.
Problem 20 Average rate of change of sine ★★★
For f(x) = sin x, find the average rate of change from 0 to π/2 and from π/2 to π, to the nearest hundredth, and explain the sign.
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