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Law Incorporation [45]
2 years ago
14

For each question below, use the function f (x) = x3

Mathematics
2 answers:
Tomtit [17]2 years ago
6 0

Answer:

A. The function is negative on the interval (-∞, 0)

B. The only root is x = 0

C. The function approaches ∞ when x gets really large (goes towards ∞). The function approaches -∞ when x gets really small (goes towards -∞).


Step-by-step explanation:

The function given is f(x)=x^3

<em>The graph is attached. Looking at the graph will make understanding the solutions easier.</em>


A.

We need to find the intervals that is divided by the roots of the function.

To find x-intercepts, we set f(x)=0

f(x)=x^3\\0=x^3\\x=0

<em>*Looking at the graph, we can also see that x=0 is the only x-intercept* </em>

Thus the intervals are from -∞ to 0 and from 0 to ∞

We take value in each interval to determine whether the function is negative or positive. If the answer is positive, function is increasing, if negative, the function is decreasing.

  • From -∞ to 0, we take x = -1

f(-1)=(-1)^3\\=-1

Hence it is decreasing

  • From 0 to ∞, we take x = 1

f(1)=(1)^3\\=1

Hence it is increasing


The function is negative on the interval (-∞, 0)


B.

To find the roots, x-intercepts, we set f(x)=0

f(x)=x^3\\0=x^3\\x=0

The only root is x = 0


C.

To find end behavior, we look at the graph.

<em><u>The end behavior means what happens to the function when x goes to ∞ and -∞</u></em>

Looking at the graph, the function approaches ∞ when x gets really large (goes towards ∞). The function approaches -∞ when x gets really small (goes towards -∞).

<em>*Also, if you plug in large x values, f(x) goes towards infinity. If you plug in small x values, f(x) goes towards negative infinity*</em>

givi [52]2 years ago
5 0

Answer:

A. (-∞ , 0)

B. x = 0 triple root

C. The function tends to infinity

Step-by-step explanation:

For the function f(x) = x^3 we have:

Negative intervals:

(-∞ , 0)

The roots of this function is:

x = 0

The final behavior of this function tends toward infinity

A graphic is attached below


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