Question

Consider the function

g(x)=x¹². Describe the range of the function.
1: All real numbers
2: [0, [infinity])
3: (-[infinity], 0]
4: None of these

Answer 1

The range of the function g(x)=x¹² is [0, ∞), indicating that g(x) takes on only zero or positive values.

Step-by-step explanation:

The function in question is g(x)=x¹². When we examine the range of the function, we're looking at the possible values that g(x) can take for all x in the domain. Since any real number raised to an even power (such as 12) will result in a positive value or zero, and considering that x can take any real value, the range of this function is [0, ∞).

This means that the function never takes negative values, only zero or positive values. Therefore, the function will always be above or on the x-axis, never below it.