Answer:
Thus, [tex]y=-\sqrt{x+3}[/tex] represents the transformed graph on the attached figure, which is a translated square root graph i.e. vertically reflected across the y-axis and also horizontally translated or shifted 3 units to the left.
Step-by-step explanation:
Consider the function
y = f(x)
The rule of horizontal translation
y = f(x-h)
When 'h' is positive, the function is shifted to the right.
When 'h' is negative, the function is shifted to the left.
The rule of implying vertical reflection across the x-axis
y = -f(x)
Applying the rule:
We know that the square root function is
[tex]y=\sqrt{x}[/tex]
We know that if the graph would be reflected across the x-axis, then
[tex]y=-\sqrt{x}[/tex]
We know that is horizontally translated or shifted 3 units to the left, it implies +
3 inside the radical implies. Then the transformed function becomes .
Please check the attached diagram. From the diagram,
- The blue graph shows the parent function [tex]y=\sqrt{x}[/tex].
- The red graph shows the transformed function i.e. vertically reflected across the y-axis and also horizontally translated or shifted 3 units to the left.
Thus, [tex]y=-\sqrt{x+3}[/tex] represents the transformed graph on the attached figure, which is a translated square root graph i.e. vertically reflected across the y-axis and also horizontally translated or shifted 3 units to the left.
