2126 Sketch a possible graph for a function f with the specified properties. (Many

Chapter 1, Problem 21

(choose chapter or problem)

Sketch a possible graph for a function $f$ with the specified properties. (Many different solutions are possible.)

(i) the domain of $f$ is $[-1,1]$

(ii) $f(-1)=f(0)=f(1)=0$

(iii) $\lim _{x \rightarrow 1^{+}} f(x)=\lim _{x \rightarrow 0} f(x)=\lim _{x \rightarrow 1^{-}} f(x)=1$

Equation Transcription:

$f$

$\left[{-1,\ 1}\right]$

$f(-1)\ \ =\ f(0)=\ f(1)=0$

$\lim\limits_{{x} \rightarrow {{1}^{+}}}f(x)\ =\lim\limits_{{x} \rightarrow {0}}f(x)\ =\lim\limits_{{x} \rightarrow {{1}^{-}}}f(x)=1$

Text Transcription:

[-1,1]

f(-1)=f(0)=f(1)=0

lim x right arrow 1+ f(x) = lim x right arrow 0 f(x) = lim x right arrow 1- f(x) =1

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