<p>Page 57</p>
<p>Which of the following is an odd function?
I. 3x^3+5
II. 4x^6+2x^4-3x^2
III. 7x^5-8x^3+12x</p>
<p>Answer is III only.</p>
<p>I thought I is also an odd function? Is it because x^0 is not odd?
However, if you look on the previous page, it has y=3x^4+2x^2-8 as an example of an even function? why??</p>
<p>Page. 58</p>
<p>If 3x^3-9x^2+Kx-12 is divisible by x-3, then K=</p>
<p>A. -40
B. -3
C. 3
D. 4
E. 22</p>
<p>The answer Barrons says is A. because you substitute 3 for x and set equation equal to zero and solve for x. However, wouldn't that give you x=4?</p>
<p>The 0th power is considered odd, if your not sure, graph it.</p>
<p>I also think the second one is 4.</p>
<p>f(x) is odd if f(-x) = -f(x) for all x.
It means that the graph of f has rotational symmetry with respect to the origin.
f(x) is even if f(x) = f(-x) for all x.
It means that the graph of f is symmetry with respect to the y-axis.</p>
<p>The 0th power (= constant) is EVEN function. For example, if f(x) = 5, then f(-x) = 5 and f(x) = f(-x). Graphically, f(x) = 5 is symmetry w.r.t the y axis.</p>
<p>For the function f(x) = 3x^3+5, f(-x) = -3x^3 + 5 and -f(x) = -3x^3 -5
,and they are not the same. => it’s not odd function.
Also the graph of 3x^3 is symmetry with respect to the origin,i.e. odd function
but 3x^3 + 5 is not symmetry with respect to the origin because the graph has to be moved up 5 from the origin. So it’s neither even nor odd.</p>
<p>For f(x) = 3x^4+2x^2-8 , f(-x) = 3(-x)^4 + 2(-x)^2 -8 = 3x^4+2x^2-8
and f(x) = f(-x), which is even function.</p>
<p>For the second question, yes, the answer is 4.</p>