Calculus Examples
f(x)=x2+2
Step 1
Determine if the function is odd, even, or neither in order to find the symmetry.
1. If odd, the function is symmetric about the origin.
2. If even, the function is symmetric about the y-axis.
Step 2
Step 2.1
Find f(-x) by substituting -x for all occurrence of x in f(x).
f(-x)=(-x)2+2
Step 2.2
Simplify each term.
Step 2.2.1
Apply the product rule to -x.
f(-x)=(-1)2x2+2
Step 2.2.2
Raise -1 to the power of 2.
f(-x)=1x2+2
Step 2.2.3
Multiply x2 by 1.
f(-x)=x2+2
f(-x)=x2+2
f(-x)=x2+2
Step 3
Step 3.1
Check if f(-x)=f(x).
Step 3.2
Since x2+2=x2+2, the function is even.
The function is even
The function is even
Step 4
Since the function is not odd, it is not symmetric about the origin.
No origin symmetry
Step 5
Since the function is even, it is symmetric about the y-axis.
Y-axis symmetry
Step 6