Sure, let's step through the problem together.
### Step-by-Step Solution:
1. Evaluate the Function:
The function given is [tex]\( f(x) = 2^x \)[/tex].
First, let's evaluate [tex]\( f(x) \)[/tex] for each value of [tex]\( x \)[/tex] listed in the table:
- When [tex]\( x = 0 \)[/tex]:
[tex]\[
f(0) = 2^0 = 1
\][/tex]
- When [tex]\( x = 1 \)[/tex]:
[tex]\[
f(1) = 2^1 = 2
\][/tex]
- When [tex]\( x = 2 \)[/tex]:
[tex]\[
f(2) = 2^2 = 4
\][/tex]
- When [tex]\( x = 3 \)[/tex]:
[tex]\[
f(3) = 2^3 = 8
\][/tex]
- When [tex]\( x = 4 \)[/tex]:
[tex]\[
f(4) = 2^4 = 16
\][/tex]
2. Fill the Table:
Now, let's fill in these evaluated values into the table:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x)=2^x \\
\hline
0 & 1 \\
\hline
1 & 2 \\
\hline
2 & 4 \\
\hline
3 & 8 \\
\hline
4 & 16 \\
\hline
\end{array}
\][/tex]
3. List the Ordered Pairs:
The ordered pairs [tex]\((x, f(x))\)[/tex] can now be written as:
- [tex]\((0, 1)\)[/tex]
- [tex]\((1, 2)\)[/tex]
- [tex]\((2, 4)\)[/tex]
- [tex]\((3, 8)\)[/tex]
- [tex]\((4, 16)\)[/tex]
4. Graph the Ordered Pairs:
To graph these pairs, each pair represents a point on the coordinate plane. You would:
- Plot the point [tex]\((0, 1)\)[/tex]
- Plot the point [tex]\((1, 2)\)[/tex]
- Plot the point [tex]\((2, 4)\)[/tex]
- Plot the point [tex]\((3, 8)\)[/tex]
- Plot the point [tex]\((4, 16)\)[/tex]
When plotted, these points show an exponential growth curve since the value of [tex]\( f(x) \)[/tex] doubles as [tex]\( x \)[/tex] increases by 1.
### Summary:
- Evaluated [tex]\( f(x) \)[/tex] for [tex]\( x \)[/tex] values: 0, 1, 2, 3, 4.
- Filled in the table with the calculated [tex]\( f(x) \)[/tex] values.
- Listed the ordered pairs.
- These points depict the exponential growth of [tex]\( 2^x \)[/tex] when plotted on a coordinate plane.
I hope this step-by-step explanation helps you understand how to evaluate the function and plot the results!
