Question

What is the end behaviour of this radical function?
$f(x) = - 2 \sqrt[3]{x + 7}$
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Answer 1

Answer: The square root function f(x)=√x has domain [0,+∞) and the end behaviour is. as x→0 , f(x)→0. as x→∞ , f(x)→∞. Note: "end behavior"

Step-by-step explanation:

So, the sign of the leading coefficient is sufficient to predict the end behavior of the function. To predict the end-behavior of a polynomial function, first check whether the function is odd-degree or even-degree function and whether the leading coefficient is positive or negative.

Answer 2

The end behavior of the function is, when x approaches positive infinity, f(x) approaches negative infinity.

Option A is correct.

End behavior of function:

We have to find the end behavior of the given radical function.

To check end behavior, we have to check limit of function at x tends to infinity and x tends to minus infinity.

Given function are,

                   $f(x)=-2\sqrt[3]{x+7}$

We can not put $x=-\infty$, because variable under square root must be greater than equal to zero.

When we check limit at $x=\infty$.

$\lim_{x \to \infty} f(x)= \lim_{x \to \infty} -2\sqrt[3]{x+7}=-\infty$

Hence, the end behavior of the function is, when x approaches positive infinity, f(x) approaches negative infinity.

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