Question

describe the transformation (f(x) = \sqrt{x + 1} - 5) in words.

the parent function (f(x) = \sqrt{x}) has been shifted 1 unit and 5 units.

Explanation:

⚡ Using what you learned: combining transformations

Step 1: Analyze the horizontal shift

The term inside the square root is \(x + 1\).
Replacing \(x\) with \(x + h\) shifts the graph horizontally:

• If \(h > 0\), the shift is to the left.
• Here, \(h = 1\), so the graph is shifted left by \(1\) unit.

Step 2: Analyze the vertical shift

The term outside the square root is \(- 5\).
Adding or subtracting a constant \(k\) outside the function shifts the graph vertically:

• If \(k < 0\), the shift is downward.
• Here, \(k = -5\), so the graph is shifted down by \(5\) units.

Answer:

The parent function \(f(x) = \sqrt{x}\) has been shifted left 1 unit and down 5 units.