5e2f0b…: “Despite a happy lake”

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1 : Consider the function $f$ , given by the graph below.

$f$ is at $a=0$ because:

$\lim _{x\to a}f(x) = f(a)$ $\lim _{x\to a}f(x)$ does not exist $x=a$ is not in the domain of $f$ $\lim _{x\to a}f(x)$ exists but is not $f(a)$

$f$ is at $a=3$ because:

$\lim _{x\to a}f(x) = f(a)$ $\lim _{x\to a}f(x)$ does not exist $x=a$ is not in the domain of $f$ $\lim _{x\to a}f(x)$ exists but is not $f(a)$

$f$ is at $a=5$ because:

$\lim _{x\to a}f(x) = f(a)$ $\lim _{x\to a}f(x)$ does not exist $x=a$ is not in the domain of $f$ $\lim _{x\to a}f(x)$ exists but is not $f(a)$

$f$ is at $a=6$ because:

$\lim _{x\to a}f(x) = f(a)$ $\lim _{x\to a}f(x)$ does not exist $x=a$ is not in the domain of $f$ $\lim _{x\to a}f(x)$ exists but is not $f(a)$

$f$ is at $a=0$ because:

$\lim _{x\to a^{+}}f(x) = f(a)$ $\lim _{x\to a^{-}}f(x)=f(a)$ $\lim _{x\to a}f(x)$ does not exist $x=a$ is in the domain of $f$