Question

What are the domain and range of f(x)=3(x−5)²(x−5)²−8?

a) Domain: All real numbers; Range:(−8,[infinity])
b) Domain: All real numbers; Range:(−8,0)
c) Domain:x ∈ R; Range: y≥−8
d) Domain:x ∈ R; Range: y>−8

Answer 1

The domain of the function is all real numbers, and the range is y > -8.

Step-by-step explanation:

The domain of a function represents the set of all possible input values or x-values. In this case, the function f(x) = 3(x-5)²(x-5)² - 8 does not have any restrictions on the x-values, so the domain is all real numbers, which can be represented as x ∈ R.

The range of a function represents the set of all possible output values or y-values. In this case, the function f(x) = 3(x-5)²(x-5)² - 8 has a minimum value of -8. As the function is quadratic and the coefficient of the x² term is positive, the function opens upwards and approaches positive infinity. Therefore, the range can be represented as y > -8.