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Given the function, f(x)= √ x+2-3 choose the correct transformation

1) left 2, down 3
2) left 2, up 3
3) right 2, down 3
4) right 2, up 3

1 Answer

5 votes

Answer:

1) left 2, down 3

Explanation:

Given:

The function is,
f(x)=√(x+2)-3

Here, the parent function is square root function.

So, Let
g(x) be the parent function.


g(x)=√(x)

Now, in order to transform
g(x) to
f(x), first, we need to add 2 to x and is given by the rule:


g(x)\rightarrow g(x+2)=√(x+2). From the transformation rules, if a positive number is added to x, then the graph shifts left.

Hence, the graph of
g(x) will shift left by 2 units.

Now, next we need to add -3 to
g(x+2) to get the given function
f(x). The rule is given as:


g(x+2)\rightarrow g(x+2) - 3=√(x+2)-3=f(x).

As per transformation rules, if a negative number is added to the function, the graph shifts down.

Here, the graph of
g(x+2) will shift down by 3 units.

Overall, the parent function
g(x)=√(x) can be transformed to
f(x)=√(x+2)-3 by shifting the parent function graph 2 units left and 3 units down.

So, option 1 is correct.

User Galeksic
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