Question

What are the domain and range of the function f(x)= x^4-2x^2-4? domain: all real numbers range: all real numbers greater than or equal to –5 domain: all real numbers range: all real numbers greater than or equal to –4 domain: all real numbers between –2.5 and 2.5 range: all real numbers domain: all real numbers between –2.5 and 2.5 range: all real numbers greater than or equal to –5

Answer 1

The correct answer is: domain: all real numbers, range: all real numbers greater than or equal to -5.

We can see that the function is a polynomial of degree 4, which means it is defined for all real numbers. Also, as x^4 is always non-negative, the minimum value of the function occurs when x=0, and it is f(0) = -4. Therefore, the range of the function is all real numbers greater than or equal to -4. However, since the function is increasing as we move away from 0, the range is actually all real numbers greater than or equal to the minimum value of -4 plus the vertical shift of -1, which is -5.