Question

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

Explanation:

Step1: Factor out 25 from radicand

$y = \sqrt{25(x - 5)}$

Step2: Simplify the radical

$y = \sqrt{25} \cdot \sqrt{x - 5} = 5\sqrt{x - 5}$

Step3: Describe transformation from parent

Parent function is $y=\sqrt{x}$. Horizontal shift 5 right, vertical stretch by 5.

Answer:

$y = 5\sqrt{x - 5}$
The graph is the parent square root function $y=\sqrt{x}$ shifted 5 units to the right and vertically stretched by a factor of 5, with a domain of $x \geq 5$ and range of $y \geq 0$.