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Without graphing, describe the end behavior of the graph of the function.

Question 18 options:

As x → ∞, f (x) → −∞.

As x → −∞, f (x) → ∞.


As x → ∞, f (x) → −∞.

As x → −∞, f (x) → −∞.


As x → ∞, f (x) → ∞.

As x → −∞, f (x) → −∞.


As x → ∞, f (x) → ∞.

As x → −∞, f (x) → ∞.

Without graphing, describe the end behavior of the graph of the function. Question-example-1
User PRS
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1 Answer

18 votes
18 votes

Answer:

As x → ∞, f (x) → −∞

As x → −∞, f (x) → ∞.

Explanation:

Method 1:

To solve this, we can simply substitute a large number as ∞ into the equation.

For example, as x->999 (∞), f(x)->-998999000 (-∞).

as x->-999 (-∞), f(x)->995006998 (∞)

Therefore achieving your answer of

As x → ∞, f (x) → −∞

As x → −∞, f (x) → ∞.

Method 2:

We can alternatively solve this by substituting ∞ as x.

As x->∞, f(∞) = 1-2(∞)^2-(∞)^3

= 1-∞-∞

= -∞

As x->-∞, f(-∞) = 1-2(-∞)^2-(-∞)^3

= 1 +2(∞)+(∞)

= ∞

Thus, we can say

As x → ∞, f (x) → −∞

As x → −∞, f (x) → ∞.

User Tmaximini
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2.7k points