Function Notation Worksheet Answer Key – Algebra 1

Problem 1 Repeated outputs

Each input 1, 2, 3, 4 appears once, so each has exactly one output. Two inputs share the output 5, which is allowed.

Yes, it is a function.

Problem 2 Repeated input

The input 2 is paired with both 3 and 7.

No, it is not a function.

Problem 3 Evaluate a linear function

f(5) = 4(5) − 3 = 20 − 3 = 17.

f(5) = 17

Problem 4 Evaluate a quadratic

g(−3) = (−3)² + 2 = 9 + 2 = 11.

g(−3) = 11

Problem 5 Mapping diagram

Each input has one arrow: 3 → 6, 4 → 6, 5 → 9.

Domain: the inputs {3, 4, 5}. Range: the outputs used {6, 9}.

Yes; domain {3, 4, 5}, range {6, 9}

Problem 6 Vertical line test

The vertical line x = 4 meets the curve at two points, about (4, 2.8) and (4, −2.8).

No, it is not a function.

Problem 7 Evaluate with a square

f(−4) = 5(−4)² − 2(−4) + 9 = 5(16) + 8 + 9 = 80 + 17 = 97.

f(−4) = 97

Problem 8 Find the input

5 − 3x = −10, so −3x = −15 and x = 5.

Check: f(5) = 5 − 15 = −10.

x = 5

Problem 9 Substitute an expression

f(a + 1) = 2(a + 1) + 5 = 2a + 2 + 5 = 2a + 7.

f(a + 1) = 2a + 7

Problem 10 Table to rule

The outputs increase by 3 each time and f(0) = 4, so f(x) = 3x + 4.

f(10) = 3(10) + 4 = 34.

f(x) = 3x + 4; f(10) = 34

Problem 11 Interpret f(a) = b

f(8) = 120: eight seconds after takeoff, the drone is 120 feet high.

f(15) = 0: after 15 seconds the drone is at ground level, so it has landed.

120 ft at 8 s; landed at 15 s

Problem 12 Domain and range from a graph

The graph runs from x = −3 (included) to x = 5 (not included). Heights run from −2 (not included) to 2 (included).

Domain: −3 ≤ x < 5. Range: −2 < y ≤ 2.

Problem 13 Discrete domain

Burritos are counted in whole numbers, so the domain is {0, 1, 2, …, 40}. The outputs are the multiples of 7 from 0 to 280.

Domain: whole numbers 0 to 40 (discrete); range: {0, 7, 14, …, 280}

Problem 14 Continuous domain

Time can be any value from 0 to 25 minutes. At 25 minutes, V = 12(25) = 300.

Domain: 0 ≤ t ≤ 25 (continuous); range: 0 ≤ V ≤ 300 gallons

Problem 15 Ticket pricing

A(6) = 8.5(6) + 3 = 51 + 3 = 54.

8.5n + 3 = 88 gives 8.5n = 85, so n = 10.

6 tickets cost $54; $88 buys 10 tickets

Problem 16 Town population

P(10) = 12,000 + 3,500 = 15,500.

12,000 + 350t = 17,600 gives 350t = 5,600, so t = 16 (the year 2036).

The 350 is the yearly increase in people.

P(10) = 15,500; t = 16 years; 350 people per year

Problem 17 Points to a rule

The points are (0, 3), (1, 5), (2, 7), (3, 9): outputs go up by 2, and f(0) = 3, so f(x) = 2x + 3.

f(4) = 2(4) + 3 = 11.

Domain {0, 1, 2, 3}; range {3, 5, 7, 9}.

f(x) = 2x + 3; f(4) = 11

Problem 18 Thrown ball

h(1) = −16 + 64 = 48. h(2) = −64 + 128 = 64. h(4) = −256 + 256 = 0.

h(4) = 0 means the ball is back on the ground after 4 seconds, so the domain is 0 ≤ t ≤ 4. The highest point is 64 feet.

48 ft, 64 ft, 0 ft; domain 0 ≤ t ≤ 4; range 0 ≤ h ≤ 64

Problem 19 Students and buses

(a) Each student has exactly one bus, so yes.

(b) Bus 2 is paired with both Ana and Cai, so one input has two outputs. No.

Domain of (a): {Ana, Ben, Cai, Dee}; range {1, 2, 3}.

(a) yes (b) no

Problem 20 Compare two functions

f(10) = 30 − 5 = 25.

g increases by 3 each step and g(1) = 2, so g(x) = 3x − 1 and g(10) = 29.

29 − 25 = 4.

g(10) is larger, by 4