Question

question 8 of 10 which description means the same as this limit expression? (lim_{x \to -infty} f(x) = -infty) a. the graph falls on the left side. b. the graph rises on the left side. c. the graph rises on the right side. d. the graph falls on the right side.

Explanation:

The limit \(\lim_{x \to -\infty} f(x)=-\infty\) means as \(x\) approaches negative infinity (moving to the left on the x - axis), the value of \(f(x)\) approaches negative infinity (the graph goes down). So we analyze each option:

• Option A: "The graph falls on the left side" matches the meaning of \(\lim_{x \to -\infty} f(x)=-\infty\) because as \(x\) goes to \(-\infty\) (left), \(f(x)\) goes to \(-\infty\) (falls).
• Option B: If the graph rose on the left side, the limit as \(x\to-\infty\) would be \(+\infty\), not \(-\infty\), so B is wrong.
• Option C: The limit as \(x\to-\infty\) has nothing to do with the right side (which is related to \(x\to+\infty\)), so C is wrong.
• Option D: The limit as \(x\to-\infty\) has nothing to do with the right side (which is related to \(x\to+\infty\)), so D is wrong.

Answer:

A. The graph falls on the left side.