For a function �(�)f\left(x\right)f(x), the transformation is of the function and is stated in the first column. Determine the type of transformation of the function and tick the correct option.
�
(
�
)
→
�
(
�
)
f(x)→g(x)
Translate 2 units left
Translate 2 units up
Translate 2 units down
Translate 2 units right
�
(
�
)
→
�
(
�
)
−
2
f(x)→f(x)−2
�
(
�
)
→
�
(
�
−
2
)
f(x)→f(x−2)
�
(
�
)
→
�
(
�
)
+
2
f(x)→f(x)+2
Translate 2 units left
The transformation of the function is stated as follows:
f(x) → g(x)
Translate 2 units left
Translate 2 units up
Translate 2 units down
Translate 2 units right
To determine the type of transformation, we can look for any changes in the function notation. In this case, the transformation is given as f(x) → g(x). Since there is no change in the x-value (x remains the same), this indicates a translation along the y-axis.
Looking at the options:
Translate 2 units left - This option would be represented as f(x) → f(x + 2).
Translate 2 units up - This option would be represented as f(x) → f(x) + 2.
Translate 2 units down - This option would be represented as f(x) → f(x) - 2.
Translate 2 units right - This option would be represented as f(x) → f(x - 2).
The correct option is "Translate 2 units left".
To determine the type of transformation of the function, we need to analyze the given options and understand what they mean.
1. Translate 2 units left:
This means that the whole graph of the function is shifted 2 units to the left. The function g(x) becomes f(x+2).
2. Translate 2 units up:
This means that the whole graph of the function is shifted 2 units up. The function g(x) becomes f(x)+2.
3. Translate 2 units down:
This means that the whole graph of the function is shifted 2 units down. The function g(x) becomes f(x)-2.
4. Translate 2 units right:
This means that the whole graph of the function is shifted 2 units to the right. The function g(x) becomes f(x-2).
Based on the given options, it seems like option 1 corresponds to translating the function 2 units left, option 2 corresponds to translating the function 2 units up, option 3 corresponds to translating the function 2 units down, and option 4 corresponds to translating the function 2 units right.