Let
S
:=
{
−
10
,
−
5
,
0
,
5
,
10
}
and let
g
:
S
→
S
be given by the following table of values.

y

−
10

−
5

0

5

10

g
(
y
)

−
10

0

10

−
5

5

Use the table to fill in the missing values. There may be more than one correct answer, in which case you should enter your answers as a comma separated list. If there are no correct answers, enter NONE. help (numbers)

g
(
0
)
=

g
(
5
)
=

g
(

)
=
0

g
(

We are given a function \( g: S \to S \), where the set \( S = \{-10, -5, 0, 5, 10\} \), and the table provides some values of the function \( g \) corresponding to different inputs \( y \).

The table looks like this:

| \( y \)  | \( -10 \) | \( -5 \) | \( 0 \)  | \( 5 \)  | \( 10 \) |
|:-------:|:---------:|:---------:|:--------:|:--------:|:--------:|
| \( g(y) \) | \( -10 \)  | \( 0 \)   | \( 10 \) | \( -5 \) | \( 5 \)  |

We are asked to determine the following missing values:

1. \( g(0) \) — Referring to the table, we see \( g(0) = 10 \).

2. \( g(5) \) — Referring to the table, we see \( g(5) = -5 \).

3. \( g(\text{?}) = 0 \) — We need to determine which input \( y \) gives \( g(y) = 0 \). According to the table, \( g(-5) = 0 \).

### Final Answers:
1. \( g(0) = 10 \)
2. \( g(5) = -5 \)
3. \( g(\text{?}) = 0 \) — The answer is \( y = -5 \).

Would you like more details, or do you have any questions?

Here are 5 related questions for further practice:
1. What is the inverse of the function \( g \) based on the given table?
2. How many different outputs can a function from a set to itself have?
3. What is the composition of \( g \) with itself, i.e., \( g(g(y)) \) for all \( y \in S \)?
4. If we defined a new function \( f: S \to S \) as \( f(y) = -g(y) \), what would the table of \( f \) look like?
5. How does knowing the function’s behavior affect its invertibility?

**Tip**: When given a function in a table format, always match the input-output pairs carefully to spot patterns or missing values.

Let S := {-10, -5, 0, 5, 10} and let g: S → S be given by the following table of values. y −10 −5 0 5 10 g(y) −10 0 10 −5 5 Use the table to fill in the missing values. There may be more than one correct answer, in which case you should enter your answers as a comma-separated list. If there are no correct answers, enter NONE. g(0) = g(5) = g(?) = 0

Learn how to solve a function mapping problem with missing values using a table of inputs and outputs. This problem covers key concepts like functions and mappings and explores the relationship between function inputs and outputs for students in Grades 8-10.

Math Problem Statement

g ( 0 )

g ( 5 )

)

Solution

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