Provide an Appropriate Response $\mathrm { f }$ To See Whether It Appears to Have a Continuous Extension

question 280

Multiple Choice

Provide an appropriate response.
-Use a calculator to graph the function $\mathrm { f }$ to see whether it appears to have a continuous extension to the origin. If it does, use Trace and Zoom to find a good candidate for the extended function's value at $x = 0$ . If the function does not appear to have a continuous extension, can it be extended to be continuous at the origin from the right $c$ the left? If so, what do you think the extended function's value(s) should be?
$f ( x ) = \frac { 6 ^ { x } - 1 } { x }$

• A) continuous extension exists from the right; \(f ( 0 ) \approx 1.8145\)
• B) continuous extension exists at origin; \(f ( 0 ) = 0\)
• C) continuous extension exists at origin; \(f ( 0 ) \approx 1.8145\)
• D) continuous extension exists from the left; \(\mathrm { f } ( 0 ) \approx 1.8145\)

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