Let's complete the table for each function and then answer the questions that follow.
Given table:
[tex]\[
\begin{array}{|r|r|r|r|}
\hline
x & y_2=4x & y_2=4x^2 & y_3=4x \\
\hline
0 & 0 & 0 & 1 \\
\hline
1 & 4 & a & b \\
\hline
2 & c & 16 & d \\
\hline
3 & e & f & g \\
\hline
\end{array}
\][/tex]
We will find the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], [tex]\(c\)[/tex], [tex]\(d\)[/tex], [tex]\(e\)[/tex], [tex]\(f\)[/tex], and [tex]\(g\)[/tex]:
1. For [tex]\(x = 1\)[/tex]:
- For [tex]\(y_2=4x\)[/tex]: [tex]\(y_2 = 4 \times 1 = 4\)[/tex]
- For [tex]\(y_2=4x^2\)[/tex]: [tex]\(y_2 = 4 \times (1 ^ 2) = 4\)[/tex]
- For [tex]\(y_3=4x\)[/tex]: [tex]\(y_3 = 4 \times 1 = 4\)[/tex]
So, [tex]\(a = 4\)[/tex], [tex]\(b = 4\)[/tex].
2. For [tex]\(x = 2\)[/tex]:
- For [tex]\(y_2=4x\)[/tex]: [tex]\(y_2 = 4 \times 2 = 8\)[/tex]
- For [tex]\(y_3=4x\)[/tex]: [tex]\(y_3 = 4 \times 2 = 8\)[/tex]
So, [tex]\(c = 8\)[/tex], [tex]\(d = 8\)[/tex].
3. For [tex]\(x = 3\)[/tex]:
- For [tex]\(y_2=4x\)[/tex]: [tex]\(y_2 = 4 \times 3 = 12\)[/tex]
- For [tex]\(y_2=4x^2\)[/tex]: [tex]\(y_2 = 4 \times (3 ^ 2) = 36\)[/tex]
- For [tex]\(y_3=4x\)[/tex]: [tex]\(y_3 = 4 \times 3 = 12\)[/tex]
So, [tex]\(e = 12\)[/tex], [tex]\(f = 36\)[/tex], [tex]\(g = 12\)[/tex].
Completed table:
[tex]\[
\begin{array}{|r|r|r|r|}
\hline
x & y_2=4x & y_2=4x^2 & y_3=4x \\
\hline
0 & 0 & 0 & 1 \\
\hline
1 & 4 & 4 & 4 \\
\hline
2 & 8 & 16 & 8 \\
\hline
3 & 12 & 36 & 12 \\
\hline
\end{array}
\][/tex]
So, the values are:
[tex]\[ a = 4, \quad b = 4, \quad c = 8, \quad d = 8, \quad f = 36, \quad g = 12 \][/tex]
