Question
(1) Describe the transformations that occurred from the parent function, \( y=\sqrt{x} \). Then determine the new domain and range. \( \begin{array}{ll}\text { a) } y=\sqrt{x+5} & \text { b) } y=-\sqrt{x-3}\end{array} \)
Ask by Barker Wright.
Nov 12,2024 10:10
UpStudy AI Solution
Tutor-Verified Answer
Answer
a) \( y=\sqrt{x+5} \): Traslación horizontal izquierda en 5 unidades. Dominio: \( x \geq -5 \), Rango: \( y \geq 0 \).
b) \( y=-\sqrt{x-3} \): Traslación horizontal derecha en 3 unidades y reflejo sobre el eje x. Dominio: \( x \geq 3 \), Rango: \( y \leq 0 \).
Solution
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The Deep Dive
For \( y = \sqrt{x+5} \), the transformation involves a horizontal shift to the left by 5 units. This means that instead of starting from \( x=0 \) (the original domain), the new domain becomes \( x \geq -5 \). The range remains unchanged as \( y \geq 0 \).
For \( y = -\sqrt{x-3} \), the transformation includes a horizontal shift to the right by 3 units and a vertical reflection over the x-axis. The new domain is \( x \geq 3 \), and the range flips to \( y \leq 0 \), indicating that the function only takes negative values.
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