Question

1) Consider the function f(x) = 3 +8/x^-2

Answer 1

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Answer:

  a. no discontinuities

  b. (0, 3)

  c. none

  d. f(x) → +∞ for |x| → ∞

Step-by-step explanation:

The function written in this problem statement is ...

  $f(x)=3+\dfrac{8}{x^{-2}}=8x^2+3\qquad\text{a quadratic function}$

a) Polynomial functions of any degree have no discontinuities.

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b) f(0) = 3. The y-intercept is (0, 3).

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c) x² is always positive, so there are no x-intercepts

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d) The leading coefficient of this even-degree polynomial is positive, so f(x) tends toward +∞ as |x| tends toward ∞.