Analyze the graph of the following function as follows:`f(x)=-(x-1)(x+2)^3`

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embizze's profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

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Given `f(x)=-(x-1)(x+2)^3` :

(1) The y-intercept is found when x=0, thus y=-(-1)(2)^3=8 and the y-intercept is 8

The x-intercept(s) are where y=0: 0=(x-1)(x+2)^3

By the zero product property, either x-1=0 and/or (x+2)^3=0. Thus the x-intercepts are x=1 and x=-2.

(2) The e` `nd behavior is `f(x)=-x^4`` ` (See graph below). Expanding the binomials and multiplying, we see that this is a polynomial with highest degree 4 and leading coefficient -1. (Expands as `-x^4-5x^3-6x^2+4x+8` )

(3) Since this is a fourth degree polynomial, the maximum number of turning points is 4-1=3.

(4) Graph:

Graphed with y=x^4 on larger scale:

 

brianna09's profile pic

brianna09 | Student, Undergraduate | (Level 3) Honors

Posted on

sorry the rest of the problems

Analyze the graph of the following function as follows:

(a) Find the x- and y-intercepts.

(b) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|.

(c) Find the maximum number of turning points.

(d) Graph the function and submit the graph to the Dropbox.

Please show all of your work.

f(x)=-(x-1)(x+2)^3

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