Question
This table shows some values of the functions f(x) and g(x). Complete the table.
x f(x)=4x+3 g(x)=
1
3
(3)x
0 3
1
3
1 7 1
2 11 3
3 15 9
4 19 27
5
6
Now, complete the sentences about the two functions.
Of the two functions,
has greater values on the interval from
, inclusive. For some x-value between
, the graphs intersect. For every x-value greater than that,
has a greater value.
x f(x)=4x+3 g(x)=
1
3
(3)x
0 3
1
3
1 7 1
2 11 3
3 15 9
4 19 27
5
6
Now, complete the sentences about the two functions.
Of the two functions,
has greater values on the interval from
, inclusive. For some x-value between
, the graphs intersect. For every x-value greater than that,
has a greater value.
Answers
GPT-4o mini
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.
### 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.