Answer:
D, neither
Step-by-step explanation:
to determine whether a function is even, odd or neither, we need to know what it means
an even function is symmetric with respect to the y-axis
an odd function is symmetric with respect to the origin
to solve an equation to see if its even or odd, we would need to substitute <em>x</em> in the equation for <em>-x</em>.
in an even function when we substitute f(-x), it should be equal to to f(x)
in an odd function when we substitute f(-x), it should be equal to -f(x)
so lets test the function given to see if its even
f(x) = x³ + 4x
f(-x) = (-x)³ + 4(-x)
f(-x) = x³ - 4x
f(-x) = x³ - 4x ≠ f(x) = x³ + 4x
comparing this to the orignal function, we see that f(-x) = x³ - 4x is not even as we did not get the same output as the original function
now we should test to see if its odd. we have already seen what f(-x) is, now lets try -f(x) and compare it to f(-x) and f(x)
-f(x) = -(x³ + 4x) -->
-f(x) = -x³ - 4x ≠ f(-x) = x³ - 4x
f(-x) = x³ - 4x ≠ f(x) = x³ + 4x
comparing this to f(x) and f(-x), we see that it not odd as we did not get the same output
so the answer is D, neither even nor odd
reflection of f(x) about x-axis
