The piecewise function is given by t(x)= cases mx+n, & -2 x<1

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

The piecewise function

t

is given by

t(x)=\begin{cases} mx+n, & -2\le x<1,\\ x^{2}, & 1\le x<3,\\ 10-mx, & 3\le x\le 4, \end{cases}

where

m

and

n

are constants. Find the values of

m

and

n

that make

t

continuous on

[-2,4]

. Using those values, state an interval of length at most

1

inside

[2,3]

on which a solution to

t(x)=5

is guaranteed to exist.