Question
State the range of the range f(x) = 1/3x+4
Answers
GPT-4 Turbo
To determine the range of the function f(x) = (1/3)x + 4, we look at the behavior of the function as x varies over all real numbers.
Since we have a linear function where x is multiplied by a non-zero constant (1/3) and then 4 is added to it, as x takes on any real number, the value of f(x) will also take on any real number. The slope (1/3) indicates how much f(x) changes for a given change in x, and since the slope is not zero, the function is neither constant nor bounded.
Therefore, the range of f(x) is all real numbers, which we can denote as (-∞, ∞).
In interval notation, this would be written as:
Range(f(x)) = (-∞, ∞)
Since we have a linear function where x is multiplied by a non-zero constant (1/3) and then 4 is added to it, as x takes on any real number, the value of f(x) will also take on any real number. The slope (1/3) indicates how much f(x) changes for a given change in x, and since the slope is not zero, the function is neither constant nor bounded.
Therefore, the range of f(x) is all real numbers, which we can denote as (-∞, ∞).
In interval notation, this would be written as:
Range(f(x)) = (-∞, ∞)