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 $f(x) = \\left \\{ \\begin{array}{l} \\phantom{{.}} \\\\ \\phantom{{.}} \\\\ \\phantom{{.}} \\\\\\phantom{{.}} \\\\ \\phantom{{.}} \\\\ \\phantom{{.}}\\end{array} \\right .$ $\\var{p},$ $x \\leq \\var{a},$ $\\simplify{{q1}*x+{p+er1-q1*a}},$ $\\var{a} \\lt x \\leq \\var{b},$ $\\simplify{{q2}*x^2+{-2*q2*b}*x+{q2*b^2+q1*(b-a)+p+er1+er2}},$ $\\var{b}\\lt x \\leq \\var{c},$ $\\var{q2*(c-b)^2+q1*(b-a)+p+er1+er2+er3},$ $x \\gt \\var{c}.$
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$f$ is discontinuous at $x=a$ where $a=\\;$[[0]].

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{discont(a,b,c,p,q1,q2,er1,er2,er3,dis)}

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The function is discontinuous at $x=\\var{dis}$.

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At $x=\\var{dis}$ we have:

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\$\\lim_{x \\nearrow\\; \\var{dis}} f(x) \\neq \\lim_{x \\searrow\\; \\var{dis}} f(x)\$

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See graph of $f$ above.

", "statement": "

Find the point at which the following function $f:\\mathbb{R} \\rightarrow \\mathbb{R}$ is not continuous.

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", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "notes": "", "description": ""}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}