1. ## even function

I have two problems that I cannot get 100% correct! bah! let f(x)= x^2+sin(x). what is g(x) when you shift f(x) to the right 4 and up 7.

I got this: ((x-4)^2)+sin(x)+7
but the computer says it isnt right!

Second, I have to define these next graphs as Even, odd, or neither. and i swear I am getting them right, and if I'm not, could someone please explain?

sin^2x= neither
sin(x)^2= even
sin(cos(x))= odd
sin(sin(x))= even
sin(x)+cos(x)= odd

2. Originally Posted by MathNeedy18
sin^2x= neither
$\displaystyle [\sin(-x)]^2=[-\sin(x)]^2=[\sin(x)]^2$

sin(x)^2= even
sin(cos(x))= odd
$\displaystyle \sin(\cos(-x))=\sin(\cos(x))$

sin(sin(x))= even
$\displaystyle \sin(\sin(-x))=\sin(-\sin(x))=-\sin(\sin(x))$

sin(x)+cos(x)= odd

$\displaystyle \sin(-x)+\cos(-x)=-\sin(x)+\cos(x)$

RonL

3. Hello, MathNeedy18!

Let: .$\displaystyle f(x)\:= \:x^2 + \sin(x).$
What is $\displaystyle g(x)$ when you shift $\displaystyle f(x)$ to the right 4 and up 7?

I got this: .$\displaystyle (x-4)^2+ \sin(x)+7$
. . but the computer says it isn't right! . . . . It isn't
$\displaystyle \text{To shift the graph 4 units to the right,}$
. . $\displaystyle \text{replace }{\color{blue}all}\text{ the }x\text{'s with }(x-4).$

You should have had: .$\displaystyle g(x)\;=\;(x-4)^2 + \sin(x-4) + 7$