Questions: Consider the following function. q(x)=-2 sqrt(x+3)+4 Step 1 of 2: Determine the more basic function that has been shifted, reflected, stretched, or compressed. Answer f(x)=

Consider the following function.
q(x)=-2 sqrt(x+3)+4

Step 1 of 2: Determine the more basic function that has been shifted, reflected, stretched, or compressed.

Answer
f(x)=

Transcript text: Consider the following function. \[ q(x)=-2 \sqrt{x+3}+4 \] Step 1 of 2: Determine the more basic function that has been shifted, reflected, stretched, or compressed. Answer Keypad Keyboard Shortcuts \[ f(x)= \]

Solution

Solution Steps

Solution Approach

To determine the more basic function that has been transformed, we need to identify the core function before any transformations. The given function is \( q(x) = -2 \sqrt{x+3} + 4 \). The core function here is the square root function \( \sqrt{x} \). The transformations applied to this core function include a horizontal shift, a vertical shift, a vertical stretch/compression, and a reflection.

Step 1: Identify the Core Function

The given function is

\[ q(x) = -2 \sqrt{x + 3} + 4. \]

The core function before any transformations is

\[ f(x) = \sqrt{x}. \]

Step 2: Analyze the Transformations

The function \( q(x) \) can be analyzed for transformations applied to the core function \( f(x) \):

Horizontal Shift: The term \( x + 3 \) indicates a shift to the left by 3 units.
Vertical Stretch/Compression: The coefficient \(-2\) indicates a vertical stretch by a factor of 2 and a reflection across the x-axis.
Vertical Shift: The \( +4 \) indicates a shift upward by 4 units.