To find: the function is even or odd or neither using graph.
![Check Mark](/static/check-mark.png)
Answer to Problem 76E
Neither even nor odd
Explanation of Solution
Given information:
Given Function is
Concept Used:-
Odd function: - A function f(x) is said to be even if graph of function is symmetric about origin.
For example: -
Even function: - A function f(x) is said to be even if graph of function is symmetric about y-axis.
For example:-
Calculation:-
Drawing graph of function
Symmetricity about Y-axis: - If graph is symmetric about y-axis if (x, y) is on graph then (-x, y) is also on graph for all x in domain.
Since, (2, 1) is on graph but (-2, 1) (as at x = -2, g (t) = -1.5) is not on graph.
So, using graph we can see (x, y) is on graph but (-x, y) is not on graph.
And function is not symmetric about y-axis.
Symmetricity about origin: - If graph is symmetric about origin if (x, y) is on graph then (-x, -y) is also on graph for all x in domain.
But using graph we can see (1, 0) is on graph but (-1, 0) is not on graph.
That is, if (x, y) is on graph then (-x, -y) is not on graph for all values of x in domain.
So, function is not symmetric about origin.
Therefore, the given function is neither symmetric about y-axis nor about origin. So, it is neither even nor odd.
Chapter 1 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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