Answer: Choice B
The domain is {x∈R| x≠−2}
The range is {y∈R| y≠−5}
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Explanation:
Using the function, we can factor the numerator to get
x^2-x-6 = (x-3)(x+2)
Then the (x+2) terms cancel out leaving x-3 only
Therefore, f(x) simplifies to f(x) = x-3.
This produces the straight line graph that is shown. But there's a hole at (-2,-5)
Why is this? It's because plugging x = -2 into the original equation (before you simplify) leads to a division by zero error.
The denominator x+2 becomes -2+2 = 0 and we can't divide by zero.
If we plugged x = -2 into the simplified version of f(x), then we have
f(x) = x-3
f(-2) = -2-3
f(-2) = -5
Showing why the hole is at (-2,-5)
There is no way that x can equal -2, so this is why we kick it out of the domain. Similarly, there's no way to get to y = -5, and this value is kicked out of the range.
The notation x∈R means that x is in the real number set. Saying {x∈R| x≠−2} means x is any real number but -2. The range is a similar story but we kick out -5 instead.
