Question

On graph y = 2^x points (0,1),(2,4), (-1,0.5) create a table of values that would translate the function in the graph up 2 units
Table 1
x y
-1 -2.5
0 -1
1 0
2 2
Table 2
x y
-1 0.5
0 1
1 2
2 4
Table 3
x y
-1 2.5
0 3
1 4
2 6
Table 4
x y
-3 -2.5
-2 -1
-1 0
0 2

Answer 1

To translate the function \( y = 2^x \) up by 2 units, we need to add 2 to the original function. Therefore, the new function after the translation will be:

\[
y = 2^x + 2
\]

Let's evaluate this new function for the points given in the original graph and then create a table based on that.

From the points given on the original graph \( y = 2^x \):
- For \( x = -1 \):
\[
y = 2^{-1} + 2 = 0.5 + 2 = 2.5
\]
- For \( x = 0 \):
\[
y = 2^{0} + 2 = 1 + 2 = 3
\]
- For \( x = 1 \):
\[
y = 2^{1} + 2 = 2 + 2 = 4
\]
- For \( x = 2 \):
\[
y = 2^{2} + 2 = 4 + 2 = 6
\]

Now, we can create the updated table of values for the new function \( y = 2^x + 2 \):

**Translated Table:**
\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-1 & 2.5 \\
0 & 3 \\
1 & 4 \\
2 & 6 \\
\hline
\end{array}
\]

Looking at the options presented in your question, this matches **Table 3**:

**Table 3:**
\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-1 & 2.5 \\
0 & 3 \\
1 & 4 \\
2 & 6 \\
\hline
\end{array}
\]

Thus, Table 3 is the correct table representing the translated function \( y = 2^x + 2 \).