To graph the function [tex]\( f(x) = \sqrt{x} + 4 \)[/tex] using a table of values, we'll start by calculating the values of [tex]\( f(x) \)[/tex] for various values of [tex]\( x \)[/tex]. Here is the table of values we will use:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) = \sqrt{x} + 4 \\
\hline
0 & 4.0 \\
1 & 5.0 \\
2 & 5.414213562373095 \\
3 & 5.732050807568877 \\
4 & 6.0 \\
5 & 6.23606797749979 \\
6 & 6.449489742783178 \\
7 & 6.645751311064591 \\
8 & 6.82842712474619 \\
9 & 7.0 \\
10 & 7.16227766016838 \\
\hline
\end{array}
\][/tex]
This table shows the calculated values of the function [tex]\( f(x) \)[/tex] at integer values of [tex]\( x \)[/tex] ranging from 0 to 10. Next, plot these points on a graph:
1. Plot the point (0, 4.0)
2. Plot the point (1, 5.0)
3. Plot the point (2, 5.414213562373095)
4. Plot the point (3, 5.732050807568877)
5. Plot the point (4, 6.0)
6. Plot the point (5, 6.23606797749979)
7. Plot the point (6, 6.449489742783178)
8. Plot the point (7, 6.645751311064591)
9. Plot the point (8, 6.82842712474619)
10. Plot the point (9, 7.0)
11. Plot the point (10, 7.16227766016838)
After plotting these points on the coordinate plane, draw a smooth curve that passes through all the points. The curve should be a typical representation of the function [tex]\( f(x) = \sqrt{x} + 4 \)[/tex], starting from (0, 4), increasing gradually, and resembling the shape of a slightly flattened square root function shifted upwards by 4 units.
Now, compare this plot to the options A), B), and C) to select the correct graph. The correct graph should show the function starting at (0, 4) and increasing in a similar manner to the values we calculated above.
