How do I determine whether the function is even, odd, or neither. How do I describe the symmetry?
ex 1) f(t)= t&2 +2t -3
Even: Replace t to -t, and if the resulting function is still the same, that is, f(-t) = f(t), then it is even. And the graph is symmetric about the y-axis.
Odd: Replace t to -t, and if the resulting function is the negative of the original function, that is, f(-t) = -f(t), then it is odd. And the graph is symmetric about the origin.
Neither: If resulting function is neither f(x) or -f(x), then it is neither.
Solving,
f(t)= t^2 + 2t - 3
Replace t with -t:
f(-t)= (-t)^2 + 2(-t) -3
f(-t) = t^2 - 2t - 3
Therefore, it is neither.
Hope this helps~ `u`
To determine whether a function is even, odd, or neither, you need to examine its algebraic expression.
1) To check for even symmetry, you need to evaluate whether f(-t) is equal to f(t).
So, for the given function f(t) = t^2 + 2t - 3, we will compare f(-t) and f(t).
f(-t) = (-t)^2 + 2(-t) - 3
= t^2 - 2t - 3
We observe that f(-t) is different from f(t), so the given function is NOT even symmetric.
Therefore, we can conclude that the function f(t) = t^2 + 2t - 3 is neither even nor odd.
Regarding symmetry, a function can be described as symmetric about the y-axis (even), symmetric about the origin (odd), or neither symmetric. In this case, since the function is neither even nor odd, it is not symmetric about any axis.