<p>to those who have the book
for the diagnostic test in the beggining
why is the answer D
for number 2.</p>
<p>to those who don't have the book question is</p>
<p>A function is said to be even if f(x) = f(-x). Which of the following is not an even function</p>
<p>a) y= lxl
b) y= sec x
c) y= logx
d) y= x2+sin x
e) y= 3x4+2x2+ 17</p>
<p>pleasee help</p>
<p>x^2 equals (-x)^2</p>
<p>but</p>
<p>sin(x) doesn’t equal sin (-x)</p>
<p>I don’t know if that helps, I’m not good at explaining things</p>
<p>The definition of a even function is that the f(x) = f(-x)… so plug in both x and -x and if they’re equal the function is said to be even.</p>
<p>well that will take so much time
ok so sin x does not equal sin (-x)</p>
<p>does that apply for tan and cos?</p>
<p>Just do this :
Put the graph into your calculator.
If its symmetical to the y axis from 0 –> whatever # you want, then its eveb</p>
<p>Well you should just know that the Sin(x) doesn’t equal Sin(-x)… but if you don’t you should certainly know that a) and e) are even, and that c) isn’t. Then it should only take a few seconds to plug in x and -x into b) and d). There are so many ways to solve that problem, but it’s fastest if you just know sin(x) doesn’t equal sin(-x).</p>
<p>okay so sin does not equal sin (-x)</p>
<p>thanks</p>
<p>does that apply for
tan and cos too?</p>
<p>also i graphed it and they are ALL symmetric</p>
<p>elaslawek when u say graph them into the calculator u mean graph them as they are
or like plug in a number then graph</p>
<p>for D) instead of x2+sinx i graph 1(squared) + sin (1)</p>
<p>sin(x) is an odd function (f(-x)=-f(x) symmetric about the origin. You can see that a is not true because of the absolute value, b is not true because sec is one over cos except for at pi/2 and 3pi/2 where it is undefined. For c you cannot take the log of a negative number. Because of the sin(x) added to x squared, it is not even because sin(x) does not equal sin(-x) (maybe plug in pi/4 and -pi/4 to prove this). e is not right because all of the terms of the polynomial are raised to even powers. The way I did this problem was to plug in -x for x.</p>
<p>tl;dr I learned that Sin and Tan are odd, while cos is even. [precalculus]</p>