Question

Please help! I'm struggling a lot with this domain and range.

Answer 1

Answers: Choices A, D, and E

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Step-by-step explanation:

The domain is the set of allowed x inputs.

In this case, we can plug in anything but x = 2 because of the vertical asymptote here.

This means the domain is the interval notation
`(-\infty,2) \cup (2,\infty)` that notation basically says "start with the entire real number line. Then poke a hole, or remove, 2 from the number line".

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The range is the set of possible y outputs. In this case, the domain and range lead to the same interval notation since we're kicking out "2" each time. This time we focus on the horizontal asymptote. The curve gets closer and closer to these dashed lines but never actually reaches them.

Since
`(-\infty,2) \cup (2,\infty)` is one of the possible ways to represent the range, one of the answers is choice A.

The interval notation
`(-\infty,2) \cup (2,\infty)` is too vague because it's not clear if we're talking about the domain or range. The notation
`\left\{\text{y}|\text{y} \in \text{R}, \ \text{y} \\e 2\right\}` is more specific. It says "y is a real number such that it cannot equal 2". In other words "y can be anything but 2". This tells us that choice D is another answer.

So either y < 2 or y > 2 which represents us being below the horizontal asymptote or above it respectively.

The third and final answer is choice E.