Question

answer parts (a)-(e) for the function shown below. f(x)=x^3 + 2x^2 - x - 2 the x - axis and turns around. c. find the y - intercept. the y - intercept is y = - 2. (type an integer or a decimal.) d. determine whether the graph has y - axis symmetry, origin symmetry, or neither. choose the correct answer below. a. origin symmetry b. y - axis symmetry c. neither e. use the graphing tool to graph the function. if necessary, find a few additional points and graph the function. use the maximum number of turning points to check whether it is drawn correctly. click to enlarge graph

Explanation:

Step1: Recall y - axis symmetry test

Replace \(x\) with \(-x\) in \(f(x)=x^{3}+2x^{2}-x - 2\). We get \(f(-x)=(-x)^{3}+2(-x)^{2}-(-x)-2=-x^{3}+2x^{2}+x - 2\). Since \(f(-x)
eq f(x)\), the function does not have y - axis symmetry.

Step2: Recall origin symmetry test

Check if \(f(-x)=-f(x)\). \(-f(x)=-(x^{3}+2x^{2}-x - 2)=-x^{3}-2x^{2}+x + 2\). Since \(f(-x)
eq -f(x)\), the function does not have origin symmetry.

Answer:

C. neither