(Solved): Consider the function \[ f(x)=\left\{\begin{array}{ll} 5 \cdot x+9 & x-\frac{1}{5} \end{array}\righ ...

Consider the function \[ f(x)=\left\{\begin{array}{ll} 5 \cdot x+9 & x<-\frac{1}{5} \\ 9 & x=-\frac{1}{5} \\ 200 \cdot x^{2} & x>-\frac{1}{5} \end{array}\right. \] Tick all of the following statements that are correct. \( f \) is continuous at \( x=-\frac{1}{5} \). \[ \lim _{x \rightarrow\left(-\frac{1}{5}\right)^{-}} f(x)=8 \] \( f \) has a jump discontinuity at \( x=-\frac{1}{5} \). \( f \) is discontinuous at \( x=-\frac{1}{5} \). \[ \lim _{x \rightarrow-\frac{1}{5}} f(x)=f\left(-\frac{1}{5}\right) . \] \( f \) has a removable discontinuity at \( x=-\frac{1}{5} \). \[ \lim _{x \rightarrow\left(-\frac{1}{5}\right)^{+}} f(x)=9 . \] \( \lim _{x \rightarrow-\frac{1}{5}} f(x) \) exists.