54E

Step-by-step solution Step 1 of 5 We need to tell the given function graphs A,B and C are even, odd or neither. The function f (x) is even if (-x) is equa l to (x)for all x in the domain. This means that func tion f(x) is symmetric about y-axis and we can say that the function v alues for and -x are equal. Polynomials consisting of only even powers of the variable (of the form x 2n, where n is a non negative integer) are even functions. Step 2 of 5 The function f (x) is odd if (-x) is equal t f(x) for all in the domain. This means that function f(x) has symmetry with respect to the origin. Polynomials consisting of only odd 2n+1 powers of the variable (of the form x , where n is a non negative integer) are odd functions. Step 3 of 5 We can notice that fo r graph A that (-x) is e qual to f(x) for all x in the domain and the graph is symmetric about y-axis. Therefore the graph A is even.