The function is defined by h(x)= cases 1 x-4 , & x<4 [6pt] 5-x , & x 4

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

The function

h

is defined by

h(x)=\begin{cases}\dfrac{1}{x-4}, & x<4\\[6pt] \sqrt{5-x}, & x\ge4.\end{cases}

On which of the following intervals is

h

continuous? (a)

(-\infty,4)\cup[4,5]

(b)

(-\infty,4)\cup(4,5]

(c)

(-\infty,4)\cup(4,5)

(d)

(-\infty,4)\cup(4,\infty)