Final answer:
The domain of the function f(x)=3x²+5 for 0≤x≤8 is [0, 8], and the range is [5, 197]. This is because the function, which is an upward-opening parabola, produces outputs from 5 to 197 within the given domain.
Step-by-step explanation:
The domain and range of the function f(x)=3x²+5 for 0≤x≤8 can be determined by evaluating the function at the endpoints of the given interval for x. The domain is the set of all allowable x-values which, in this case, is the closed interval from 0 to 8. To find the range, we look at the outputs of the function within the domain:
f(0) = 3*(0)² + 5 = 5
f(8) = 3*(8)² + 5 = 3*64 + 5 = 192 + 5 = 197
Since the function f(x) is a parabola that opens upwards and has no maximum on the interval 0≤x≤8, the range is all f(x) values from 5 up to and including 197.
Therefore, the domain is [0, 8] and the range is [5, 197].