For an even function we have f(x) = f(-x)
In the given graphs let us substitute values
In first graph
f(2) = 0
f(-2) = 0
So f(2) = f (-2)
Graph is even
In second graph
f(2) = 0
f(-2) = 4
So f(2) ≠ f (-2)
Graph is not even
First graph represents an even function
The second function represents an even function.
A function g(x) is said to be even if g(x) = g(-x). All that is needed is to replace x with -x in each equation, simply it and assess whether the equation remains unchanged. If the equation is identical to the original one then it is said to be even.
The first graph (the parabola opening down) represents an even function, since this graph is symmetric with respect to the y-axis.
Graphs of functions that are ODD, are symmetric about the origin.
Graphs of function that are EVEN, are symmetric about y-axis.
We need to figure out which one of the 4 are EVEN. So we take y-axis as the mirror and see both sides, LEFT and RIGHT and see i the points are symmetric or not.
Graph 1, 2, 3 not symmetric about y-axis
Graph 4 Definitely every point to left side of y-axis has a corresponding mirror point to the right of y-axis. So this is an EVEN FUNCTION.
Just took the test and the answer is C. The point is at (0,4) making it even.
The person before was wrong.