Question

Which of the following equation shows the above graph?

• A. $f\left(x\right)=x^2+9$
• B. $f\left(x\right)=(x-9{)}^2$
• C. $f\left(x\right)=9-x^2$
• D. $f\left(x\right)=-|x^2+9|$
• E. $f\left(x\right)=|-x^2+9|$

Answer 1

The correct option is E $f\left(x\right)=|-x^2+9|$

At $x=-3,3$ , $f\left(x\right)$ should be zero . check this condition with all options.
We can observe that except option $C,E$ , every option will eliminate.
Now observe that for $x>3$ , option $C$ will be negative, but it should be positive as per the given graph.
So, the correct answer is option $E$.