Back to Interpret key features of graphs — Problem 5 · Task Set 7

HSF.IF.B.4 Tutor Intake — Key Features of Graphs

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Grade 9·12 problems·~14 min·Common Core Math - HS Functions·group·hsf-if-b-4

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Procedures

A graph of $f(x) = x^2 - 4$ is shown in a small window from $x = -3$ to
$x = 3$ . In the window, the graph appears to level off at the right edge
near $y = 5$ .

A student says: "The end behavior is that $f(x)$ approaches 5 as $x$
increases, because that's where the graph ends."

What is wrong with this reasoning?

Nothing — the end behavior is correctly described by where the graph stops
at the edge of the viewing window.

End behavior describes the trend as $x \to \pm\infty$ , not what happens at
the edge of the window. For $f(x) = x^2 - 4$ , as $x \to +\infty$ ,
$f(x) \to +\infty$ .

End behavior only applies to linear and exponential functions, not to
quadratics.

The student is correct; the end behavior depends on the viewing window
chosen.