Select the correct answer.
The parent square root function, , is transformed to create function .

Which statement is true?
A. The graph of is translated 3 units to the left and 4 units down.
C. The graph of is translated 4 units to the right and 3 units down.
D. The graph of is translated 4 units to the left and 3 units up.
D is translated 3 units to the right and 4 units up.

Ask by Patel Fowler. in the United States

Mar 31,2025

Question

Select the correct answer.
The parent square root function, , is transformed to create function .

Which statement is true?
A. The graph of is translated 3 units to the left and 4 units down.
C. The graph of is translated 4 units to the right and 3 units down.
D. The graph of is translated 4 units to the left and 3 units up.
D is translated 3 units to the right and 4 units up.

Ask by Patel Fowler. in the United States

Mar 31,2025

UpStudy AI · Accepted Answer

To solve the problem, we start with the parent function:

$$
f(x)=\sqrt{x}
$$

The transformed function is given as:

$$
g(x)=\sqrt{x+3}-4
$$

Step 1: Identify the horizontal translation.  
Inside the square root, we have $$x+3$$. In general, if the function has an expression $$\sqrt{x+h}$$, the graph of $$ f(x) $$ is shifted $$h$$ units to the left (if $$h$$ is positive) or to the right (if $$h$$ is negative). Here, $$h=3$$ means the graph of $$ f(x) $$ is shifted 3 units to the left.

Step 2: Identify the vertical translation.  
After the square root, we have $$-4$$. This indicates that the graph is shifted 4 units downwards.

Therefore, the graph of $$ f(x)=\sqrt{x} $$ is translated 3 units to the left and 4 units down to obtain $$ g(x)=\sqrt{x+3}-4 $$.

The correct statement is:  
A. The graph of $$ f $$ is translated 3 units to the left and 4 units down.
The graph of $$ f $$ is translated 3 units to the left and 4 units down to obtain $$ g(x) $$.

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