Continuity at a Point

Explore the conditions under which a function [math]f\left(x\right)[/math] is continuous at a point [math]x_0[/math] in the domain of [math]f[/math].
Ready, Set, Practice!
If [math]\lim_{ x \to x_0 }f(x)[/math] exists and is finite, then [math]f\left(x\right)[/math] is continuous at [math]x_0[/math].[br]True or false?[br]Justify your answer, providing a counterexample if appropriate.
Given a function [math]f(x)[/math], whose domain is [math]D[/math], we know that [math]\lim_{ x \to x_0^- }f(x)=\lim_{ x \to x_0^+ }f(x)[/math] and that [math]x ∉D[/math].[br]Is the function continuous at [math]x_0[/math]?[br]Justify your answer, providing a counterexample if appropriate.
Describe the continuity of the function shown in the graph below.[br][br][img]data:image/png;base64,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[/img][br][br][br]
Determine the domain of the function [math]f\left(x\right)=\sqrt{4-x}[/math] and verify analytically that it is continuous at [math]x_0=3[/math], then plot the graph of the function and observe its behaviour in the neighbourhood of [math]x_0=3[/math].[br][br]How can you use a graph to check if a function is continuous?
Plot the graph of the function [math]f(x) = \begin{cases} x+2 & \text{ if } x <1 \\ -x+1 & \text{ if } x \geq 1 \end{cases}[/math] and explain whether it is continuous at [math]x_0=1[/math].
Find the value of the parameter [math]a\in\mathbb{R}[/math] that makes the piecewise function [math]g(x) = \begin{cases} -x^2-4x-3 & \text{ if } x \leq -1 \\ 1+\frac{a}{x^2} & \text{ if } x>-1 \end{cases}[/math] continuous at [math]x_0=-1[/math].[br]Plot the graph of the continuous function that you have obtained.
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Information: Continuity at a Point