Question

part 1 of 2
rewrite the function to make it easy to graph using transformations of its parent function. describe the graph.
$y = \sqrt{25x - 125} - 5$
$y = \square$ (simplify your answer.)

Explanation:

Step1: Factor inside the square root

Factor 25 from the radicand:
$\sqrt{25x - 125} = \sqrt{25(x - 5)}$

Step2: Simplify the square root

Use $\sqrt{ab}=\sqrt{a}\sqrt{b}$ for $a\geq0,b\geq0$:
$\sqrt{25(x - 5)} = \sqrt{25}\sqrt{x - 5} = 5\sqrt{x - 5}$

Step3: Rewrite the original function

Substitute back into the original equation:
$y = 5\sqrt{x - 5} - 5$

Answer:

$y = 5\sqrt{x - 5} - 5$

Graph Description (additional):

The parent function is $y=\sqrt{x}$. This transformed graph is:

1. Horizontally shifted 5 units to the right,
2. Vertically stretched by a factor of 5,
3. Vertically shifted 5 units downward.

The domain is $x\geq5$ and the range is $y\geq-5$.