QuestionFind the end behavior of the function $h(x) = -4x^2 + 11$ as $x$ approaches $\pm \infty$ .

Studdy Solution

STEP 1

Assumptions1. The function is $h(x) = -4x^{} +11$ . We are asked to find the end behavior of the function as $x$ approaches negative infinity and positive infinity.

STEP 2

The end behavior of a function can be determined by looking at the leading term of the function. In this case, the leading term is $-4x^{2}$ .

STEP 3

Because the leading term is $-x^{2}$ , the end behavior of the function will be determined by this term.

STEP 4

The degree of the leading term is2, which is even. Therefore, the end behavior of the function will be the same as $x$ approaches both negative infinity and positive infinity.

STEP 5

The coefficient of the leading term is -4, which is negative. Therefore, as $x$ approaches both negative infinity and positive infinity, $h(x)$ will approach negative infinity.

STEP 6

So, the end behavior of the function $h(x) = -4x^{2} +11$ isAs $x$ approaches negative infinity, $h(x)$ approaches negative infinity. As $x$ approaches positive infinity, $h(x)$ approaches negative infinity.

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QuestionFind the end behavior of the function $h(x) = -4x^2 + 11$ as $x$ approaches $\pm \infty$ .

Studdy Solution

STEP 1

Assumptions1. The function is $h(x) = -4x^{} +11$ . We are asked to find the end behavior of the function as $x$ approaches negative infinity and positive infinity.

STEP 2

The end behavior of a function can be determined by looking at the leading term of the function. In this case, the leading term is $-4x^{2}$ .

STEP 3

Because the leading term is $-x^{2}$ , the end behavior of the function will be determined by this term.

STEP 4

The degree of the leading term is2, which is even. Therefore, the end behavior of the function will be the same as $x$ approaches both negative infinity and positive infinity.

STEP 5

The coefficient of the leading term is -4, which is negative. Therefore, as $x$ approaches both negative infinity and positive infinity, $h(x)$ will approach negative infinity.

STEP 6

So, the end behavior of the function $h(x) = -4x^{2} +11$ isAs $x$ approaches negative infinity, $h(x)$ approaches negative infinity. As $x$ approaches positive infinity, $h(x)$ approaches negative infinity.

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QuestionFind the end behavior of the function h(x)=−4x2+11h(x) = -4x^2 + 11h(x)=−4x2+11 as xxx approaches ±∞\pm \infty±∞.

Studdy Solution

STEP 1

Assumptions1. The function is h(x)=−4x+11h(x) = -4x^{} +11h(x)=−4x+11 . We are asked to find the end behavior of the function as xxx approaches negative infinity and positive infinity.

STEP 2

The end behavior of a function can be determined by looking at the leading term of the function. In this case, the leading term is −4x2-4x^{2}−4x2.

STEP 3

Because the leading term is −x2-x^{2}−x2, the end behavior of the function will be determined by this term.

STEP 4

The degree of the leading term is2, which is even. Therefore, the end behavior of the function will be the same as xxx approaches both negative infinity and positive infinity.

STEP 5

The coefficient of the leading term is -4, which is negative. Therefore, as xxx approaches both negative infinity and positive infinity, h(x)h(x)h(x) will approach negative infinity.

STEP 6

So, the end behavior of the function h(x)=−4x2+11h(x) = -4x^{2} +11h(x)=−4x2+11 isAs xxx approaches negative infinity, h(x)h(x)h(x) approaches negative infinity. As xxx approaches positive infinity, h(x)h(x)h(x) approaches negative infinity.

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QuestionFind the end behavior of the function $h(x) = -4x^2 + 11$ as $x$ approaches $\pm \infty$ .

Assumptions1. The function is $h(x) = -4x^{} +11$ . We are asked to find the end behavior of the function as $x$ approaches negative infinity and positive infinity.

The end behavior of a function can be determined by looking at the leading term of the function. In this case, the leading term is $-4x^{2}$ .

Because the leading term is $-x^{2}$ , the end behavior of the function will be determined by this term.

The degree of the leading term is2, which is even. Therefore, the end behavior of the function will be the same as $x$ approaches both negative infinity and positive infinity.

The coefficient of the leading term is -4, which is negative. Therefore, as $x$ approaches both negative infinity and positive infinity, $h(x)$ will approach negative infinity.

So, the end behavior of the function $h(x) = -4x^{2} +11$ isAs $x$ approaches negative infinity, $h(x)$ approaches negative infinity. As $x$ approaches positive infinity, $h(x)$ approaches negative infinity.