The function h (t) = - 4.92t^2+17.69t+575 is used to model an object being tossed from a tall building, where h (t) is the height in meters and t is the time in seconds. Rounded to the nearest hundredth, what are the domain and range? domain: [0, 12.76] range: [1.8, 590.9] domain: [1.80,1276] range: [1.8, 590.9] domain: [1.80,12.76] range: [0, 590.9] domain: [0, 12.76] range: [0, 590.9]

We have the following equation:

h (t) = - 4.92t^2+17.69t+575

For the domain we have:

We match zero:

-4.92t ^ 2 + 17.69t + 575 = 0

We look for the roots:

t1 = - 9.16

t2 = 12.76

We are left with the positive root, so the domain is:

[0, 12.76]

For the range we have:

We derive the function:

h ' (t) = - 9.84t + 17.69

We equal zero and clear t:

-9.84t + 17.69 = 0

t = 17.69 / 9.84

t = 1.80

We evaluate the time in which it reaches the maximum height in the function:

h (1.80) = - 4.92 * (1.80) ^ 2 + 17.69 * (1.80) + 575

h (1.80) = 590.90

Therefore, the range is given by:

[0, 590.9]

Answer:

the domain and range are:

domain: [0, 12.76] range: [0, 590.9]