Question

Hi if someone could explain the right answer that would be great i’m totally lost!!

Answer 1

Answer:

A. lim [x ⇒ -∞] g(x) = -5 . . . . . . written in text form, not typeset

Step-by-step explanation:

A horizontal asymptote is a line that the function approaches but never reaches. It represents the limiting value that the function can have. (The function can come as close to that value as you like for some value of x, but can never actually reach that value.)

Here, you're told the asymptote for negative x values is -5. That means g(x) gets closer and closer to -5 for values of x that are more and more negative. That is, as x approaches infinity, g(x) approaches -5. We say -5 is the limit of g(x) as x approaches negative infinity.

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The attached graph shows a function that has characteristics like those of g(x).

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This question is about vocabulary: what is the meaning of "asymptote" and "limit", and how do you read a description of a limit written using math language.