Question

The graph of g(x) = (x + 2)2 is a translation of the graph of f(x) by units.
1. Left 2. 2 units
3. Right 4. 3 units
EDGE 21

Answer 1

Answer:

Left 2 units

Step-by-step explanation:

Without knowing what f(x), it is impossible to answer this question. I'll answer assuming a parent function of $f(x)=x^2$.

In the function $y=(x-c)^2$, $c$ represents the phase shift from parent function $f(x)=x^2$. If $c$ is positive (e.g. $(x-3)^2$), then the function shifts to the right however many units $c$ is. If $c$ is negative (e.g. $(x+5)^2$), the function shifts to the left however many units the absolute value of $c$ is.

In the function $g(x)=(x+2)^2$, let's find out the value of $c$:

Format: $y=(x-c)^2$

$g(x)=(x+2)^2=(x-(-2))^2$

Therefore, $c=-2$.

Since $c$ is negative, the function must shift to the left. To find out how many units it shifts to the left, take the absolute value of $c$:

$|-2|=\boxed{2\text{ units to the left}}$.

Thus, the graph of $g(x)=(x+2)^2$ is a translation of the graph $f(x)=x^2$ by 2 units to the left.

*Note: Once again, this answer is assuming $f(x)=x^2$ as it is not clarified in the question. If $f(x)\neq x^2$ and is already shifted, you will need to account for shift. If you believe this is the case, feel free to let me know in the comments.