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ella [17]
3 years ago
7

Write the equation of a piecewise function with a jump discontinuity at x =3. Then, determine which step of the 3-step test for

continuity that the function
fails.

Mathematics
1 answer:
seraphim [82]3 years ago
5 0

Answer:

Here's a possible example:

Step-by-step explanation:

f(x) =\begin{cases} x & \quad x < 3\\x+3 & \quad x \geq 3\\\end{cases}

Each piece is linear, so the pieces are continuous by themselves.

We need consider only the point at which the pieces meet (x = 3).

\displaystyle \lim_{x \longrightarrow 3^{-}} f(x) = \lim_{x \longrightarrow 3^{-}} x = 3\\\\\displaystyle \lim_{x \longrightarrow 3^{+}} f(x) = \lim_{x \longrightarrow 3^{+}} x+3 = 6\\\\f(3) = x + 3 = 6\\\\\displaystyle \lim_{x \longrightarrow 3^{-}} f(x) \neq f(3)

The left-hand limit does not equal ƒ(x), so there is a jump discontinuity at x =3.

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