Question

Question 3 Create a polynomial which has the following zeros: x = -2,4,7. Explain the behavior of your polynomial as x++ and as x .00. If necessary, plot the polynomial in order to validate your answers. Question 4 Describe the end behavior of the function below by stating whether f(x) as x- 00 f(x) = -26 Question 5 Describe the end behavior of the function below by stating whether f(x) - coas x- 00 f(x) = 5x3 + 8.07

Answer 1

3. Given the zeros are x = -2, x = 4 and x = 7

Therefore, (x + 2), (x - 4) and (x - 7) are the factors of f(x)

Thus,

f(x) = a(x + 2)(x - 4)(x - 7)

Let us assume the leading coefficient is 1 i.e,. a = 1

Therefore,

f(x) = (x + 2)(x - 4)(x - 7)

The degree of the function f(x) is 3 i.e. odd and the leading coefficient is 1 i.e. positive

Therefore,

As x -> + $\infty$ , f(x) -> + $\infty$

As x -> - $\infty$ , f(x) -> - $\infty$

4. f(x) = - x⁶

The degree of the function f(x) is 6 i.e. even and the leading coefficient is -1 i.e. negative

Therefore, the end behavior is as below:

As x -> + $\infty$ , f(x) -> - $\infty$

As x -> - $\infty$ , f(x) -> - $\infty$

5. f(x) = 5x³ + 8x⁷

The degree of the function f(x) is 7 i.e. odd and the leading coefficient is 8 i.e. positive

Therefore, the end behavior is as below:

As x -> + $\infty$ , f(x) -> + $\infty$

As x -> - $\infty$ , f(x) -> - $\infty$