Consider the function s(x)= cases ax+1, & x<1

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

Problem

Consider the function s(x)={ax+1,x<1,bx2,1≤x<3,10−x,x≥3,s(x)= \begin{cases} ax+1, & x<1,\\ bx^{2}, & 1\le x<3,\\ 10-x, & x\ge 3, \end{cases} where aa and bb are constants. For which ordered pair (a,b)(a,b) is ss free of jump discontinuities on the interval (−∞,∞)(-\infty,\infty)? (a) (43,73)\left(\dfrac{4}{3},\dfrac{7}{3}\right) (b) (−29,79)\left(-\dfrac{2}{9},\dfrac{7}{9}\right) (c) (79,79)\left(\dfrac{7}{9},\dfrac{7}{9}\right) (d) (−49,59)\left(-\dfrac{4}{9},\dfrac{5}{9}\right)

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