Question

Graph the function using the techniques of​ shifting, compressing,​ stretching, and/or reflecting. Start with the graph of the basic function shown below.
h left parenthesis x right parenthesis equals StartRoot x plus 6 EndRoot
Question content area bottom left
Part 1
-14
14
-10
10
x
y
y equals StartRoot x EndRoot



A coordinate system has a horizontal x-axis labeled from negative 14 to 14 in increments of 2 and a vertical y-axis labeled from negative 10 to 10 in increments of 2. The graph of the function starts at (0,0) and continues up and to the right.
.
.
.
Question content area right
Part 1
Choose the correct graph below.
A.
-14
14
-10
10
x
y



A coordinate system has a horizontal x-axis labeled from negative 14 to 14 in increments of 2 and a vertical y-axis labeled from negative 10 to 10 in increments of 2. The graph of the function starts at (0,negative 6) and continues up and to the right in the shape of a square root function.
B.
-14
14
-10
10
x
y



A coordinate system has a horizontal x-axis labeled from negative 14 to 14 in increments of 2 and a vertical y-axis labeled from negative 10 to 10 in increments of 2. The graph of the function starts at (6,0) and continues up and to the right in the shape of a square root function.
C.
-14
14
-10
10
x
y



A coordinate system has a horizontal x-axis labeled from negative 14 to 14 in increments of 2 and a vertical y-axis labeled from negative 10 to 10 in increments of 2. The graph of the function starts at (0,6) and continues up and to the right in the shape of a square root function.
D.
-14
14
-10
10
x
y

Answer 1

To identify the correct graph for the function \( h(x) = \sqrt{x + 6} \), we need to analyze the effects of the transformations on the basic square root function \( y = \sqrt{x} \).

1. **Basic Function**: The graph of \( y = \sqrt{x} \) starts at the point (0, 0) and increases to the right.

2. **Transformation**: The function \( h(x) = \sqrt{x + 6} \) shifts the graph of \( y = \sqrt{x} \) horizontally.

- The "+6" inside the square root indicates a horizontal shift to the **left** by 6 units.

3. **Starting Point**: Because of the horizontal shift, the graph of \( h(x) \) will start at the point \( (-6, 0) \) instead of \( (0, 0) \).

4. **Graph Characteristics**: After this shift, the graph will continue to rise to the right, similar to the basic square root function.

Now, let's evaluate the options provided:

- **Option A**: Starts at (0, -6) – incorrect starting point.
- **Option B**: Starts at (6, 0) – incorrect starting point.
- **Option C**: Starts at (0, 6) – incorrect starting point.
- **Option D**: If the description matches with a correct representation for the transformed function, it should indicate that it starts at (-6, 0).

Since none of the options explicitly describes starting at (-6, 0), it seems like there's a mismatch. However, based on the descriptions, the graph that looks close to these transformations and follows the square root function's characteristics would likely be **closest to Option A** considering it might represent an unlisted starting point adjustment in the descriptions.

If there is nothing to match the expected result, please confirm with the specific options if adjustments are necessary or if a new option should have been included.