Questions: Graph the following function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function. Be sure to show at least three key points. Find the domain and the range of the function. h(x) = sqrt(-x) - 3

Solution Steps

The basic function is \( f(x) = \sqrt{x} \).

The given function is \( h(x) = \sqrt{-x} - 3 \). This involves:

• Reflecting \( \sqrt{x} \) over the y-axis to get \( \sqrt{-x} \).
• Shifting the graph down by 3 units.

For the basic function \( f(x) = \sqrt{x} \), key points are:

• \( (0, 0) \)
• \( (1, 1) \)
• \( (4, 2) \)

Applying the transformations:

• Reflecting over the y-axis: \( (0, 0) \), \( (-1, 1) \), \( (-4, 2) \)
• Shifting down by 3 units: \( (0, -3) \), \( (-1, -2) \), \( (-4, -1) \)

• Domain: \( x \leq 0 \)
• Range: \( y \geq -3 \)

Final Answer