Let's break down the given function [tex]\( f(x) = \frac{1}{2} x + \frac{3}{2} \)[/tex] and compare it to the value table provided and the statements.
Given value table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $f(x)$ \\
\hline
-1 & 1 \\
\hline
0 & \frac{3}{2} \\
\hline
1 & 2 \\
\hline
2 & \frac{5}{2} \\
\hline
\end{tabular}
\][/tex]
We need to check the validity of the following statements:
1. [tex]\( f\left(-\frac{1}{2}\right) = -2 \)[/tex]
2. [tex]\( f(0) = \frac{3}{2} \)[/tex]
3. [tex]\( f(1) = -1 \)[/tex]
4. [tex]\( f(2) = 1 \)[/tex]
5. [tex]\( f(4) = \frac{7}{2} \)[/tex]
Using the given results:
[tex]\[
\begin{align*}
f\left(-\frac{1}{2}\right) & = 1.25 \\
f(0) & = 1.5 \\
f(1) & = 2.0 \\
f(2) & = 2.5 \\
f(4) & = 3.5
\end{align*}
\][/tex]
Now let's compare these results with the provided statements:
1. [tex]\( f\left(-\frac{1}{2}\right) = -2 \)[/tex]: Given result is 1.25, so this statement is false.
2. [tex]\( f(0) = \frac{3}{2} \)[/tex]: Given result is 1.5 ([tex]\(\frac{3}{2}\)[/tex]), so this statement is true.
3. [tex]\( f(1) = -1 \)[/tex]: Given result is 2.0, so this statement is false.
4. [tex]\( f(2) = 1 \)[/tex]: Given result is 2.5, so this statement is false.
5. [tex]\( f(4) = \frac{7}{2} \)[/tex]: Given result is 3.5 ([tex]\(\frac{7}{2}\)[/tex]), so this statement is true.
Thus, the true statements are:
- [tex]\( f(0) = \frac{3}{2} \)[/tex]
- [tex]\( f(4) = \frac{7}{2} \)[/tex]
Hence, the correct statements that are true of the given function are:
- [tex]\( f(0) = \frac{3}{2} \)[/tex]
- [tex]\( f(4) = \frac{7}{2} \)[/tex]
