Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Several problems ask for interpretation of f(a) = b with units, and the last six are multi-step: tickets, population, a thrown ball and a comparison of two functions.
Standards: F-IF.A.1, F-IF.A.2, F-IF.B.5 · Level: Grade 9 Algebra 1
Problem 1 Repeated outputs ★★★
Is the relation {(1, 5), (2, 5), (3, 8), (4, 9)} a function? Explain.
Problem 2 Repeated input ★★★
Is the relation {(2, 3), (2, 7), (5, 1)} a function? Explain.
Problem 3 Evaluate a linear function ★★★
If f(x) = 4x − 3, find f(5).
Problem 4 Evaluate a quadratic ★★★
If g(x) = x2 + 2, find g(−3).
Problem 5 Mapping diagram ★★★
Is the mapping a function? State the domain and the range.
Problem 6 Vertical line test ★★★
Does the graph show y as a function of x? Use the vertical line test.
Problem 7 Evaluate with a square ★★★
A function is defined by f(x) = 5x2 − 2x + 9. Compute f(−4).
Problem 8 Find the input ★★★
If f(x) = 5 − 3x, find x when f(x) = −10.
Problem 9 Substitute an expression ★★★
If f(x) = 2x + 5, write f(a + 1) in simplest form.
Problem 10 Table to rule ★★★
A function has the table:
| x | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| f(x) | 4 | 7 | 10 | 13 |
Write a rule for f(x) and find f(10).
Problem 11 Interpret f(a) = b ★★★
Let f(t) be the height in feet of a drone t seconds after takeoff. Interpret f(8) = 120 and f(15) = 0.
Problem 12 Domain and range from a graph ★★★
Find the domain and the range of the function graphed. Use inequalities.
Problem 13 Discrete domain ★★★
A food truck sells burritos for $7 each and can make at most 40 per day, so C(n) = 7n. Describe the domain and the range. Is the domain discrete or continuous?
Problem 14 Continuous domain ★★★
A tank fills at 12 gallons per minute for 25 minutes, so V(t) = 12t with 0 ≤ t ≤ 25. State the domain and range and whether the domain is discrete or continuous.
Problem 15 Ticket pricing ★★★
The cost in dollars of n concert tickets is A(n) = 8.50n + 3, which includes a $3 service fee. Find A(6), find n when A(n) = 88, and interpret both results.
Problem 16 Town population ★★★
A town’s population is P(t) = 12,000 + 350t people t years after 2020. Find P(10), find when the population reaches 17,600 and interpret the 350.
Problem 17 Points to a rule ★★★
The graph shows four points of a function. Write a rule, state the domain and range of these points and predict f(4).
Problem 18 Thrown ball ★★★
The height in feet of a ball t seconds after it is thrown is h(t) = −16t2 + 64t. Find h(1), h(2) and h(4), interpret h(4) = 0 and give a sensible domain and range.
Problem 19 Students and buses ★★★
The diagram pairs students with the bus they ride. (a) Is it a function from students to buses? (b) Is the reverse relation, from buses to students, a function? Explain.
Problem 20 Compare two functions ★★★
Let f(x) = 3x − 5. A second function g has g(1) = 2, g(2) = 5 and g(3) = 8, with outputs continuing the same pattern. Which function has the larger value at x = 10, and by how much?
