Question

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

a. Where is f(x) going to have discontinuities and how do you know?


b. What is the y-intercept for f(x) and how do you know?

c.
What is the x-intercept for f(x) and how do you know?


d. What is the end behavior for f(x) and how do you know?

No links or anything like that.

Answer 1

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Answer:

a. no discontinuities

b. (0, 3)

c. none

d. f(x) → +∞ for |x| → ∞

Explanation:

The function written in this problem statement is ...

`f(x)=3+(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 ∞.