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(Solved): Consider the following. \[ f(x)=\left\{\begin{array}{ll} 6-2 x, & x \leq 3 \\ x^{2}-8, & x>3 \end{a ...
Consider the following. \[ f(x)=\left\{\begin{array}{ll} 6-2 x, & x \leq 3 \\ x^{2}-8, & x>3 \end{array}\right. \] Describe the interval(s) on which the function is continuous. (Enter your answer using interval notation.) Identify any discontinuities. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) \[ x= \] If the function has any discontinuities, identify the conditions of continuity that are not satisfied. (Select all that apply. Select each choice There is a discontinuity at \( x=c \) where \( f(c) \) is not defined. There is a discontinuity at \( x=c \) where \( \lim _{x \rightarrow c} f(x)+f(c) \). There is a discontinuity at \( x=c \) where \( \lim _{x \rightarrow c} f(x) \) dces not exist. There are no discontinuities; \( f(x) \) is continuous.