Answer:
Option: B is the correct answer
B. [tex]g(x)=-5(x+1)^2[/tex]
Step-by-step explanation:
We are given a parent function f(x) as:
[tex]f(x)=x^2[/tex]
We know that when a function is shifted k units to the left then the transformation is given by:
f(x) →f(x+k)
and when a function is vertically stretched by a factor of a then the transformation is given by:
f(x) → a f(x)
and when the reflection of function f(x) is done over the x-axis then the rule of transformation is:
f(x) → -f(x)
Hence, we will go through the transformation one by one
This means that:
f(x) → f(x+1)
- Vertically stretch by a factor of 5.
This means that:
f(x+1) → 5 f(x+1)
- and lastly reflect over the x-axis
Hence, we get transformation as:
5 f(x+1) → -5f(x+1)
Hence, we get the resultant function as:
[tex]g(x)=-5(x+1)^2[/tex]
