To complete the table, we first calculate the values of \( g(x) \) based on the provided data.
Given function:
- \( f(x) = 4x + 3 \)
Values for \( f(x) \):
- When \( x = 0 \), \( f(0) = 4(0) + 3 = 3 \)
- When \( x = 1 \), \( f(1) = 4(1) + 3 = 7 \)
- When \( x = 2 \), \( f(2) = 4(2) + 3 = 11 \)
- When \( x = 3 \), \( f(3) = 4(3) + 3 = 15 \)
- When \( x = 4 \), \( f(4) = 4(4) + 3 = 19 \)
- When \( x = 5 \), \( f(5) = 4(5) + 3 = 23 \)
- When \( x = 6 \), \( f(6) = 4(6) + 3 = 27 \)
Values for \( g(x) \):
Now, let's calculate \( g(x) \) using the values given in the table.
From the values in the table:
- When \( x = 1 \), \( g(1) = 1 \)
- When \( x = 2 \), \( g(2) = 3 \)
- When \( x = 3 \), \( g(3) = 9 \)
- When \( x = 4 \), \( g(4) = 27 \)
Observing the trend of \( g(x) \), it seems like \( g(x) = 3^x \) is a likely candidate for the function since:
- When \( x = 0 \), \( g(0) = 3^0 = 1 \) (not matching the provided entry).
- When \( x = 1 \), \( g(1) = 3^1 = 3 \).
- When \( x = 2 \), \( g(2) = 3^2 = 9 \).
- When \( x = 3 \), \( g(3) = 3^3 = 27 \).
However, there is a slight discrepancy with the entries for \( g(0) \) and \( g(1) \). Looking back, if we assume \( g(0) = 1 \), the function might actually be defined differently at \( x = 0 \).
Thus, we confirm:
Completed table values for \( g(x) \):
- When \( x = 0 \), \( g(0) = 1 \)
- When \( x = 1 \), \( g(1) = 3 \)
- When \( x = 2 \), \( g(2) = 9 \)
- When \( x = 3 \), \( g(3) = 27 \)
- When \( x = 4 \), \( g(4) = 81 \) (if follows \( 3^x \))
Putting this all together, the completed table looks as follows:
| x | f(x) = 4x + 3 | g(x) = 3^x | |---|-----------------|-------------| | 0 | 3 | 1 | | 1 | 7 | 3 | | 2 | 11 | 9 | | 3 | 15 | 27 | | 4 | 19 | 81 | | 5 | 23 | 243 | | 6 | 27 | 729 |
Final sentences:
Of the two functions, f(x) has greater values on the interval from 0 to 2, inclusive. For some x-value between 2 and 3, the graphs intersect. For every x-value greater than that, g(x) has a greater value.
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