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For the graph of y = x^4 -6x^2 +12 discuss its? symmetry, indicate whether the graph...

For the graph of y = x^4 -6x^2 +12 discuss its? symmetry, indicate whether the graph crosses the? x-axis at each? x-intercept, and determine whether y?? or y--> -? as x?? and x?-?.

1. Which symmetry would the graph of this equation? illustrate? Choose the correct letter of the answer below?

A. The graph of the function has neither type of symmetry.

B. The graph of the function is symmetric about the? y-axis.

C. The graph of the function is symmetric about the origin.

2. Find the? x-intercept(s) and determine whether the graph of the function crosses the? x-axis at each ?x-intercept. Choose the correct letter from below and fill in blanks please.

A.The graph crosses the? x-axis at the? x-intercept(s) ____ and touches but does not cross the?x-axis at the? x-intercept(s) ________.

B.The graph touches but does not cross the? x-axis at the? x-intercept(s) __________.

C.The graph crosses the? x-axis at the? x-intercept(s) ___________.

D.The graph does not have any? x-intercepts.

3. Lastly, Find the behavior of the given graph as x ? ? and x ???.

THANKS!

Solutions

Expert Solution

For the graph of y = x^4 -6x^2 +12  

1. Which symmetry would the graph of this equation? illustrate? Choose the correct letter of the answer below?

Clearly the x and -x for the graph is same, so y-axis is an axis of symmetry

f(x) = f(-x) so function is even and symmetric about y-axis

Answer B. The graph of the function is symmetric about the? y-axis.

2. Find the? x-intercept(s) and determine whether the graph of the function crosses the? x-axis at each ?x-intercept. Choose the correct letter from below and fill in blanks please.

x^4-6x^2+12

roots : x^2 = (6 + sqrt(36 - 48))/2, (6 - sqrt(36 - 48))/2 = 3 - isqrt{3}, 3 + isqrt{3}

no real solutions, so graph doesn't intersect x-axis

D.The graph does not have any? x-intercepts.

3. Lastly, Find the behavior of the given graph as x ? ? and x ???.

As can be seen, at all the large values (positive and negative), function will output only large values.

milcah answered 1 year ago
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