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I need help with number 10. I have questions about the extreme and end behavior and symmetry

I need help with number 10. I have questions about the extreme and end behavior and-example-1
User Ilise
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1 Answer

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16 votes

Answers:

Symmetry: about the origin

Extrema: No

End behavior: as x --> ∞, f(x) --> ∞ and as x --> -∞, f(x) --> -∞

Step-by-step explanation:

The graph for f(x) = x³ is

Then, we can see that the graph is symmetric over the origin becuase

f(-x) = -f(x)

(-x)³ = -(x³)

-x³ = -x³

On the other hand, it doesn't have an extreme value, there are no maximum or minimum points in a given interval.

Finally, we can see that when x increases, f(x) increases, and when x decreases f(x) decreases. So, the end behavior is

as x --> ∞, f(x) --> ∞

as x --> -∞, f(x) --> -∞

I need help with number 10. I have questions about the extreme and end behavior and-example-1
User Tom Carr
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2.4k points