Which of the following power functions has a Ushaped graph F

Which of the following power functions has a U-shaped graph? F(x) = x^3 g(x) = x^4 h(x) = x^8 m(x) = x^11

Solution

We see that at x=0 , all functions are 0

If you see the values of these functions at x=1 , they are:f(1)=1, g(1)=1,h(1)=1 and m(1)=1

Now, lets see the values at x=-1, they are : f(-1)=-1 (i.e below the x axis because of -ve y) , g(-1)=1,h(-1)=1,m(-1)=-1

We see that g(x) and h(x) are both 1 at x=1 and x=-1

therefore, it shows that both g(x) and h(x) will be symmetrical about the y axis. i.e they never have a negative value for any x but they have same values when x is positive of negative x. Thus, they have the U