document.write( "Question 1020730: Let f be a continuous function such that f(-1) = -1 and f(1) = 1.
\n" ); document.write( "Classify each of the following
\n" ); document.write( "statements as:
\n" ); document.write( "A - ALWAYS TRUE
\n" ); document.write( "N - NEVER TRUE
\n" ); document.write( "S - SOMETIMES TRUE - true in some cases, false in others
\n" ); document.write( "Justify each. Explain.\r
\n" ); document.write( "\n" ); document.write( "a. f(0) = 0
\n" ); document.write( "b. For some x with -1 <= x <= 1, f(x) = 0
\n" ); document.write( "c. For all x with -1 <= x < 1, -1 <= f(x) <=1
\n" ); document.write( "d. Given any y in [-1,1], then y = f(x) for some x in [-1,1].
\n" ); document.write( "e. If x < -1 or x >1, then f(x) < -1 or f(x) > 1
\n" ); document.write( "f . f(x) = -1 for x < 0 and f(x) = 1 for x > 0 \n" ); document.write( "

Algebra.Com's Answer #636588 by richard1234(7193) $\"\"$ $\"About$

You can put this solution on YOUR website!
a) Sometimes true (f(0) need not be 0)
\n" ); document.write( "b) Always true, by continuity/intermediate value theorem
\n" ); document.write( "c) Sometimes true, f could jump outside the interval [-1,1]
\n" ); document.write( "d) Always true, also holds from intermediate value theorem
\n" ); document.write( "e) Sometimes true, we don't know anything about f
\n" ); document.write( "f) Never true, since f is discontinuous at x = 0 \n" ); document.write( "

\n" );