To graph the function [tex]\( f(x) = \sqrt{x} + 4 \)[/tex], we need to determine the values of [tex]\( f(x) \)[/tex] for different [tex]\( x \)[/tex] values. Below is a table of values that we can use to visualize this function:
| [tex]\( x \)[/tex] | [tex]\( f(x) = \sqrt{x} + 4 \)[/tex] |
|--------|----------------------------|
| 0.0 | 4.0 |
| 1.0 | 5.0 |
| 2.0 | 5.414213562 |
| 3.0 | 5.732050808 |
| 4.0 | 6.0 |
| 5.0 | 6.236067977 |
| 6.0 | 6.449489743 |
| 7.0 | 6.645751311 |
| 8.0 | 6.828427125 |
| 9.0 | 7.0 |
| 10.0 | 7.16227766 |
Let's plot these points:
1. At [tex]\( x = 0 \)[/tex], [tex]\( f(x) = 4 \)[/tex].
2. At [tex]\( x = 1 \)[/tex], [tex]\( f(x) = 5 \)[/tex].
3. At [tex]\( x = 2 \)[/tex], [tex]\( f(x) \approx 5.414 \)[/tex].
4. At [tex]\( x = 3 \)[/tex], [tex]\( f(x) \approx 5.732 \)[/tex].
5. At [tex]\( x = 4 \)[/tex], [tex]\( f(x) = 6 \)[/tex].
6. At [tex]\( x = 5 \)[/tex], [tex]\( f(x) \approx 6.236 \)[/tex].
7. At [tex]\( x = 6 \)[/tex], [tex]\( f(x) \approx 6.449 \)[/tex].
8. At [tex]\( x = 7 \)[/tex], [tex]\( f(x) \approx 6.646 \)[/tex].
9. At [tex]\( x = 8 \)[/tex], [tex]\( f(x) \approx 6.828 \)[/tex].
10. At [tex]\( x = 9 \)[/tex], [tex]\( f(x) = 7 \)[/tex].
11. At [tex]\( x = 10 \)[/tex], [tex]\( f(x) \approx 7.162 \)[/tex].
Now, when you plot these points on a graph, you will get a curve that starts at (0, 4) and increases as [tex]\( x \)[/tex] increases. This graph is characterized by a square root function shifted upward by 4 units.
Observe the given graphs in options A, B, and C. The correct graph should show an upward trend starting from [tex]\( y = 4 \)[/tex] at [tex]\( x = 0 \)[/tex] and increasing gradually.
Thus, the correct graph should depict these characteristics. Ensure that you match this trend with the graph that aligns with these points. Given the information, you would likely select the graph that accurately reflects the increasing nature of [tex]\( f(x) = \sqrt{x} + 4 \)[/tex].
