Respuesta :
Answer:
1) left 2, down 3
Step-by-step explanation:
Given:
The function is, [tex]f(x)=\sqrt{x+2}-3[/tex]
Here, the parent function is square root function.
So, Let [tex]g(x)[/tex] be the parent function.
∴ [tex]g(x)=\sqrt{x}[/tex]
Now, in order to transform [tex]g(x)[/tex] to [tex]f(x)[/tex], first, we need to add 2 to x and is given by the rule:
[tex]g(x)\rightarrow g(x+2)=\sqrt{x+2}[/tex]. From the transformation rules, if a positive number is added to x, then the graph shifts left.
Hence, the graph of [tex]g(x)[/tex] will shift left by 2 units.
Now, next we need to add -3 to [tex]g(x+2)[/tex] to get the given function [tex]f(x)[/tex]. The rule is given as:
[tex]g(x+2)\rightarrow g(x+2) - 3=\sqrt{x+2}-3=f(x)[/tex].
As per transformation rules, if a negative number is added to the function, the graph shifts down.
Here, the graph of [tex]g(x+2)[/tex] will shift down by 3 units.
Overall, the parent function [tex]g(x)=\sqrt{x}[/tex] can be transformed to [tex]f(x)=\sqrt{x+2}-3[/tex] by shifting the parent function graph 2 units left and 3 units down.
So, option 1 is correct.
