Question

Which option correctly describes the transformation of f(x)=2x+3−−−−√−4
to g(x)=2x+8−−−−√−4
?(1 point)
Responses

shift right 5 units
shift right 5 units

shift up 5 units
shift up 5 units

shift left 5 units
shift left 5 units

shift left 8 units

Answer 1

To analyze the transformation from \( f(x) = \sqrt{2x + 3} - 4 \) to \( g(x) = \sqrt{2x + 8} - 4 \), we need to focus on the changes made to the inside of the square root function.

1. **Examine the expressions inside the square roots**:
- In \( f(x) \): The expression inside the square root is \( 2x + 3 \).
- In \( g(x) \): The expression inside the square root is \( 2x + 8 \).

2. **Compare the two expressions**:
- To go from \( 2x + 3 \) to \( 2x + 8 \), we can set:
\[
2x + 3 + k = 2x + 8
\]
where \( k \) is a constant that indicates the amount of a horizontal shift.

3. **Solve for \( k \)**:
- Rearranging gives us:
\[
k = 8 - 3 = 5
\]
- This means that to change \( f(x) \) to \( g(x) \), we effectively change the \( +3 \) to \( +8 \).

4. **Determine the nature of the shift**:
- Since we have \( 2x + 3 \) changing to \( 2x + 8 \), this indicates a shift to the left.
- A constant added to \( x \) inside the function shifts the graph to the left when the form is \( ax + b \).

Thus, the transformation from \( f(x) \) to \( g(x) \) is a **shift left 5 units**.

The correct response is:
**shift left 5 units**.