Question

Describe the geometrical transformation and write the approximate value with working ​

Answer 1

`\boxed{\text{a) Translation 5 units up; b)}\approx 110}\\`

Explanation:

a) Mapping the graphs

Mapping one graph (A) onto another (B) means that each vertical line through a point in A intersects the graph of the B at only one point.

In the diagram, the graph of ƒ(x) = √(x² + 9) is the blue line and the graph of g(x) = 5 + √(x² + 9) is in green.

Each vertical line through ƒ(x) intersects g(x) in only one point.

For example, a vertical line from (4, 0) intersects ƒ(x) at (4, 5) and g(x)

at (4, 10).

Every point in g(x) is five units higher than the corresponding point in ƒ(x).

Thus, mapping ƒ(x) onto g(x) is a translation of five units upward.

b) Integration

`\int_(2)^(11){(\sqrt{x^(2)+9}})dx\approx 65\\`

`\int_(2)^(11){(5 + \sqrt{x^(2)+9})}dx \approx [5x]_2^(11)+65\\`

`\approx (55 - 10) + 65 \approx 45 + 65\\`

`\boxed{\approx 110}\\`