Answered

IDNLearn.com is your go-to resource for finding answers to any question you have. Discover reliable and timely information on any topic from our network of knowledgeable professionals.

Use the Symmetry of a Function to Find Coordinates.

For the even function [tex]\( f \)[/tex]:

[tex]\[
a = \square
\][/tex]

\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$f(x)$[/tex] \\
\hline
-2 & 4 \\
\hline
0 & 5 \\
\hline
2 & [tex]$a$[/tex] \\
\hline
3 & 7 \\
\hline
\end{tabular}

For the odd function [tex]\( g \)[/tex]:

[tex]\[
b = \square
\][/tex]

\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$g(x)$[/tex] \\
\hline
-2 & [tex]$b$[/tex] \\
\hline
0 & 0 \\
\hline
2 & -3 \\
\hline
3 & -4 \\
\hline
\end{tabular}

Sagot :

GinnyAnsweridn
To solve the problem, we need to use the properties of even and odd functions.

### Even Function: [tex]\( f(x) \)[/tex]
An even function, [tex]\( f(x) \)[/tex], satisfies the condition:
[tex]\[ f(x) = f(-x) \][/tex]

Given the values for [tex]\( f \)[/tex]:
[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $f(x)$ \\ \hline -2 & 4 \\ \hline 0 & 5 \\ \hline 2 & $a$ \\ \hline 3 & 7 \\ \hline \end{tabular} \][/tex]

To find [tex]\( a \)[/tex], we use the property:
[tex]\[ f(2) = f(-2) \][/tex]

From the table, [tex]\( f(-2) = 4 \)[/tex]. Therefore:
[tex]\[ f(2) = 4 \][/tex]
Hence:
[tex]\[ a = 4 \][/tex]

### Odd Function: [tex]\( g(x) \)[/tex]
An odd function, [tex]\( g(x) \)[/tex], satisfies the condition:
[tex]\[ g(x) = -g(-x) \][/tex]

Given the values for [tex]\( g \)[/tex]:
[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $g(x)$ \\ \hline -2 & $b$ \\ \hline 0 & 0 \\ \hline 2 & -3 \\ \hline 3 & -4 \\ \hline \end{tabular} \][/tex]

To find [tex]\( b \)[/tex], we use the property:
[tex]\[ g(-2) = -g(2) \][/tex]

From the table, [tex]\( g(2) = -3 \)[/tex]. Therefore:
[tex]\[ g(-2) = -(-3) = 3 \][/tex]
Hence:
[tex]\[ b = 3 \][/tex]

### Summary of Results
- The value of [tex]\( a \)[/tex] is:
[tex]\[ a = 4 \][/tex]
- The value of [tex]\( b \)[/tex] is:
[tex]\[ b = 3 \][/tex]

Thus, the coordinates for the missing values have been determined as follows:
[tex]\[ a = 4 \][/tex]
[tex]\[ b = 3 \][/tex]
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com is committed to providing the best answers. Thank you for visiting, and see you next time for more solutions.