14. (08.07 MC) A polynomial function is shown below: f(x) = x3 − 4x2 − x + 4 Which graph best represents the function? (5 points) Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, 2, and 3. The graph intersects the y axis at a point between 10 and 15. Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, 2, and 3. The graph intersects the y axis at a point between 15 and 20. Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, 1, and 3. The graph intersects the y axis at a point between 5 and 10. Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 1, 1, and 4. The graph intersects the y axis at a point between 0 and 5.

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kudzordzifrancis kudzordzifrancis · Answer 1 · 2019-05-16T14:59:49+02:00

ANSWER

See attachment.

EXPLANATION

The given cubic function is:

[tex]f(x) = {x}^{3} - 4 {x}^{2} - x + 4[/tex]

We can factor by grouping to get:

[tex]f(x) = {x}^{2} ( x - 4)- 1(x - 4)[/tex]

[tex]f(x) = ( {x}^{2} - 1) ( x - 4)[/tex]

[tex]f(x) = ( {x} - 1)(x + 1) ( x - 4)[/tex]

This function will have x-intercepts at

x=-1, x=1, and x=4

The y-intercept is at where x=0.

(0,4)

The graph rises on the left and rises on the right because the degree is odd and the coefficient of the leading term is positive.