Question

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What is the range of f(x)?

–∞ < f(x) < ∞
–∞ < f(x) ≤ 4
f(x)
f(x)

Answer 1

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.

Answer 2

Answer: Choice B) f(x)

Note that f(x) is the same as 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.