Answer:
The correct answer is: Right by 3 units.
Explanation:
The quadratic functions f(x) and g(x) are described in the table.
x f(x) g(x)
−2 4 64
−1 1 49
0 0 36
1 1 25
2 4 16
3 9 9
4 16 4
5 25 1
6 36 0
In which direction and by how many units should f(x) be shifted to match g(x)?
Left by 18 units
Right by 18 units
Left by 6 units
Right by 6 units
ChatGPT
To determine the direction and magnitude of the shift needed to match the functions f(x) and g(x), we need to observe the change in x-values for each corresponding y-value in the table.
Let's compare the two functions f(x) and g(x):
x | f(x) | g(x) | Difference (f(x) - g(x))
−2 | 4 | 64 | 4 - 64 = -60
−1 | 1 | 49 | 1 - 49 = -48
0 | 0 | 36 | 0 - 36 = -36
1 | 1 | 25 | 1 - 25 = -24
2 | 4 | 16 | 4 - 16 = -12
3 | 9 | 9 | 9 - 9 = 0
4 | 16 | 4 | 16 - 4 = 12
5 | 25 | 1 | 25 - 1 = 24
6 | 36 | 0 | 36 - 0 = 36
From the differences calculated above, we can observe the pattern. As we move from left to right in the table, the differences decrease and then start to increase again. The smallest difference occurs when x = 3, and after that point, the differences increase symmetrically.
The smallest difference is 0, which means that f(3) = g(3). Therefore, to match the functions f(x) and g(x), we need to shift f(x) by 3 units to the right.