14. In the direction does the graph of $$ y=\sqrt{x+a} $$ shift as the value of a decreases? a. upward to the left.

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UpStudy AI · Accepted Answer

As the value of $$ a $$ decreases in the function $$ y = \sqrt{x + a} $$, the graph undergoes a horizontal shift. Here's how it works:

1. **Understanding the Transformation:**
   - The general form $$ y = \sqrt{x - h} $$ shifts the graph **h units to the right** if $$ h $$ is positive.
   - In your case, the function is $$ y = \sqrt{x + a} $$, which can be rewritten as $$ y = \sqrt{x - (-a)} $$. This indicates a shift of $$ -a $$ units.

2. **Effect of Decreasing $$ a $$:**
   - **Decreasing $$ a $$** means that $$ a $$ becomes more negative.
   - Since the shift is by $$ -a $$, making $$ a $$ more negative results in a larger positive shift.
   - Therefore, the graph moves **to the right** as $$ a $$ decreases.

3. **Graphical Interpretation:**
   - Imagine $$ a = 2 $$: The graph shifts **2 units to the left**.
   - If $$ a $$ decreases to $$ 1 $$, the shift becomes **1 unit to the left**.
   - Continuing this trend, if $$ a $$ becomes negative, the shift moves to the **right**.

**Conclusion:**
As the value of $$ a $$ decreases, the graph of $$ y = \sqrt{x + a} $$ shifts **to the right**.

**Answer:** As a decreases, the graph shifts horizontally to the right.
As $$ a $$ decreases, the graph of $$ y = \sqrt{x + a} $$ shifts to the right.

In the direction does the graph of shift as the
value of a decreases?
a. upward
to the left.

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In the direction does the graph of shift as the value of a decreases? a. upward to the left.