Question

Need help as soon as possible!

What is the range of f(x)?

{ f(x)| –∞ < f(x) < ∞}
{ f(x)| –∞ < f(x) ≤ 4}
{ f(x)| 4 < f(x) < ∞}
{ f(x)| 0 ≤ f(x) < ∞}

Answer 1

Answer: Choice B) { f(x)| –∞ < f(x) ≤ 4}

Note that { f(x)| –∞ < f(x) ≤ 4} is the same as { f(x)|  f(x) ≤ 4} and that's saying "the output y is at most 4". So the largest y can get is 4. This is the upper limit or ceiling so to speak. The value of y can be any number less than 4.

The range is basically the set of all possible y outputs of a function. It is the set of all y coordinates of the points on the function curve. The highest we can go is y = 4. There is no limit on how low the points can go, so it goes off to negative infinity.

Answer 2

First, we can see that $f(x) = 4$ until x = 0. It doesn't get any higher, meaning that 4 is likely the highest $f(x)$ gets. If we keep moving left to right, we can see that $f(x)$ continues to get lower and lower. Since it continues to get lower and lower. We can thus assume $f(x)$ is going to continue to get lower and lower, or approach $- \infty$.

Thus, we can say the range of $f(x)$ is the second answer choice, $- \infty < f(x) \leq 4$, since the lowest $f(x)$ gets is $- \infty$ and the highest it gets is 4.