Zoom out

$\newenvironment {prompt}{}{} \newcommand {\ungraded }[0]{} \newcommand {\todo }[0]{} \newcommand {\oiint }[0]{{\large \bigcirc }\kern -1.56em\iint } \newcommand {\mooculus }[0]{\textsf {\textbf {MOOC}\textnormal {\textsf {ULUS}}}} \newcommand {\npnoround }[0]{\nprounddigits {-1}} \newcommand {\npnoroundexp }[0]{\nproundexpdigits {-1}} \newcommand {\npunitcommand }[1]{\ensuremath {\mathrm {#1}}} \newcommand {\sagemath }[0]{\textsf {SageMath}} \newcommand {\surfaceColor }[0]{violet} \newcommand {\surfaceColorTwo }[0]{redyellow} \newcommand {\sliceColor }[0]{greenyellow} \newcommand {\vector }[1]{\left \langle #1\right \rangle } \newcommand {\sectionOutcomes }[0]{} \newcommand {\HyperFirstAtBeginDocument }[0]{\AtBeginDocument } \newcommand {\descriptionlabel }[1]{\hspace {\labelsep }\textbf {#1:}}$

Two young mathematicians discuss what curves look like when one “zooms out.”

Check out this dialogue between two calculus students (based on a true story):

Devyn: Riley, think about this function: $f(x) = \frac {x^2-2}{x^{2}+2}.$
Riley: Hmmm. If you plot it, the graph looks like this:
Devyn: Right! What I’ve noticed is that if $x$ gets big, then our function looks like a horizontal line.
Riley: I wonder how we find the line?

Guess the $y$ -intercept of this line. Come back and check your answer after reading the Dig-In!

Answers may vary.