Problem

For \(h(x)~=~2\sqrt{x~+~4}~+~1\), where \(x\) is seconds on a timeline and \(h\) is meters, state the endpoint with units, interpret the input boundary and output extremum, and give the domain and range.

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Endpoint: (4 seconds, 1 meter). Input boundary: earliest timeline value x=4. Output extremum: minimum height 1 meter. Domain: [4,∞) seconds. Range: [1,∞) meters.

Endpoint: (−4 seconds, 1 meter). Input boundary: latest timeline value x=−4. Output extremum: maximum height 1 meter. Domain: (−∞,−4] seconds. Range: (−∞,1] meters.

Endpoint: (−4 seconds, −1 meter). Input boundary: earliest timeline value x=−4. Output extremum: minimum height −1 meter. Domain: [−4,∞) seconds. Range: [−1,∞) meters.

Endpoint: (−4 seconds, 1 meter). Input boundary: earliest timeline value x=−4. Output extremum: minimum height 1 meter. Domain: [−4,∞) seconds. Range: [1,∞) meters.

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For \(h(x)~=~2\sqrt{x~+~4}~+~1\), where \(x\) is seconds on a timeline and \(h\) is meters, state the endpoint with units, interpret the input boundary and output extremum, and give the domain and range.

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