Answer: Choice B
domain: (-∞, ∞); range: f(x) ≥ 3
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Step-by-step explanation:
The domain is the set of allowed x values. We can replace x with any real number in this case. So x is between -∞ and ∞
We can write -∞ < x < ∞ which turns into the interval notation (-∞, ∞)
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The range is the set of all possible y outputs of a function.
The smallest |x| can get is 0, and the same goes for |x-4| as well.
This means the smallest f(x) = |x-4|+3 can get is y = 0+3 = 3
Hence y ≥ 3, which is the same as saying f(x) ≥ 3
f(x) = 3 or f(x) > 3
I recommend using a tool like Desmos to graph out f(x) = |x-4|+3, and you'll see the lowest point occurs when y = 3.