Question

As x approaches - ∞, y approaches ∞

True or false ?

need help!

Answer 1

The given statement is False because as x approaches
`\(-\infty\)`, the dominant term in the function
`\(f(x) = -x^3 + x^3 + 2x^2\)` is
`\(-x^3\)`, leading to
`\(-\infty\)` for y, not
`\(\infty\)`.

As x approaches negative infinity in the function
`\(f(x) = -x^3 + x^3 + 2x^2\)`, the term
`\(-x^3\)` dominates.

Since
`\(x^3\)` and
`\(2x^2\)` become negligible compared to
`\(-x^3\)`, the overall behavior of the function is driven by the cubic term.

As x decreases without bound,
`\(-x^3\)` approaches negative infinity, resulting in a divergent behavior for y, not approaching positive infinity.

Therefore, the statement "As x approaches
`\(-\infty\)`, y approaches
`\(\infty\)`" is false for this function.