Is it a function? Inputs, outputs, domain and range

Answer Key - Grade 8 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. Read this first

   Use the table

   input: x	output: y
   1 1/2	6
   -3	2
   4	6
   0	-5
   -1	9
   2	8

2. 1.

   Zee solves a puzzle-club table with six rows (and one very sharp pencil). Is it a function, and why?

   • No: inputs 1 1/2 and 4 share the output 6
   • Yes: inputs -3, -1, 0, 1 1/2, 2 and 4 each have one output
   • No: the outputs do not change by the same amount
3. 2.

   (4, -2), (-3, 5), (4, -2), (1, 0), (-3, 6). Two inputs repeat in Esme's list of points. One repeat is harmless; one is not. Is it a function, and why?

   • No: input -3 has two outputs, 5 and 6
   • Yes: inputs -3, 1 and 4 each have an output
   • No: input 4 appears in two pairs
4. 3.

   Jun plots six points in all four quadrants for a star map. Is it a function, and why?

   • No: (2, -4) and (2, 1) are on one up-and-down line
   • Yes: no two points are at the same height
   • No: the points are in all four quadrants of the grid
5. 4.

   Luz plots five points from a mystery rule, then squints at them. Is it a function, and why?

   • No: (3, -3) and (3, 2) are on one up-and-down line
   • No: (-4, 1) and (0, 1) are at the same height
   • No: the points do not go through (0, 0), so it fails
6. 5.

   The pond was 14°C at 9 a.m., 19°C at noon and 14°C at 6 p.m. Milo makes temperature the input and time the output. Is it a function, and why?

   • No: the times are not evenly spaced, so the rule fails
   • Yes: every temperature has a time
   • No: 14°C goes with two times, 9 a.m. and 6 p.m.
7. 6.

   On a winter day it was -2°C at 6 a.m., 5°C at noon and -2°C at 9 p.m. Noah makes time the input and temperature the output. Is it a function, and why?

   • No: 6 a.m. and 9 p.m. share -2°C
   • Yes: each time has just one temperature
   • No: the temperature goes up, then comes back down
8. 7.

   Ren plots five stops on a hiking map grid. What is the domain (all the inputs)? List each value once.

   -4, -1, 0, 3, 5
9. 8.

   Esme plots points from a rule, and one point is in the wrong spot. This graph is not a function. Which input has two different outputs?

   -2
10. 9.

    Kira's pairs make a function: (-2, 5), (0, 1), (3, 5), (7, -4). Which new pair can join and keep it a function?

    • (4, 1)
    • (0, 3)
    • (7, 5)
11. 10.

    Luz's pairs make a function: (-5, -2), (-1, 3), (2, 0), (6, 3). Which new pair can join and keep it a function?

    • (2, 6)
    • (1, -2)
    • (-1, -2)