Question

Complete the table.

f(x) = |2x + 1| + 1
x f(x)
–3
–1
1
3

Answer 1

To complete the table for the function \( f(x) = |2x + 1| + 1 \), we need to evaluate \( f(x) \) at the given values of \( x \).

1. For \( x = -3 \):
\[
f(-3) = |2(-3) + 1| + 1 = |-6 + 1| + 1 = |-5| + 1 = 5 + 1 = 6
\]

2. For \( x = -1 \):
\[
f(-1) = |2(-1) + 1| + 1 = |-2 + 1| + 1 = |-1| + 1 = 1 + 1 = 2
\]

3. For \( x = 1 \):
\[
f(1) = |2(1) + 1| + 1 = |2 + 1| + 1 = |3| + 1 = 3 + 1 = 4
\]

4. For \( x = 3 \):
\[
f(3) = |2(3) + 1| + 1 = |6 + 1| + 1 = |7| + 1 = 7 + 1 = 8
\]

Now, we can complete the table:

\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-3 & 6 \\
-1 & 2 \\
1 & 4 \\
3 & 8 \\
\hline
\end{array}
\]