Determine whether the function fis even odd or neither even

Determine whether the function fis even, odd, or neither even Odd neither sketch the graph of f. If fis even or odd, use symmetry to sketch its graph.

Solution

a) f(x) = x^8+x

if we put x = -x, we get

f(-x) = x^8-x

So, function is neither odd or even and graph is option D ( second row second graph)

b) f(x) = x^9-x

if we put x = -x, we get

f(-x) = -x^9+x = -(x^9-x)

So, function is odd and graph is option A

c) f(x) = 5-x^(1/9)

if we put x = -x, we get

f(-x) = 5+x^(1/9)

So, function is neither odd or even and graph is option C