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

Question

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 \( y = 2^x + 2 \).