function graph

[markgians]

I can't understand why these two graphs are different, I just picked the sign out of the parenthesis

 

[Harry_the_cat]

Compare the graphs of $\displaystyle y=-(x)^2$ and $\displaystyle y = (-x)^2$. The same thing is happening. The two functions are not equal.

 

[HallsofIvy]

$(-1)^2= 1$ NOT $-(1)^2= -1$.

 

[Dr.Peterson]

I can't understand why these two graphs are different, I just picked the sign out of the parenthesis



View attachment 29475

Here is what happens if you "pull out the sign" from g:

$$(-x+2)^\frac{2}{3} = (-1(x-2))^\frac{2}{3} = (-1)^\frac{2}{3}(x-2)^\frac{2}{3} = (1)(x-2)^\frac{2}{3} = (x-2)^\frac{2}{3}$$
On its way outside, the -1 has to pass through the 2/3 power, which makes it positive!

 

[Steven G]

Is (2*3)^3 = 2*3^3? I just picked out the 2 from the parenthesis.
Dr Peterson showed exactly what happens to that 1 in the previous post. Look at it carefully.