What is an even function? A function f is an even function if f(-x) = f(x) for all x in the domain of f.
For example f(x) = x^{2} is an even function
f(-4) = (-4)^{2} = -4 × -4 = 16 and f(4) = (4)^{2 }= 4 × 4 = 16
f(-4) = f(4) = 16
f(-3) = (-3)^{2} = = -3 × -3 = 9 and f(3) = (3)^{2 }= 3 × 3 = 9
f(-3) = f(3) = 9
f(-1) = (-1)^{2} = -1 × -1 = 1 and f(1) = (1)^{2 }= 1 × 1 = 1
f(-1) = f(1) = 1
In general, let x represent any number in the domain of f.
Then, f(-x) = (-x)^{2} = -x × -x = x^{2} and f(x) = x^{2}
f(-x) = f(x) = x^{2}
For f(-4) = f(4) = 16, the points are (-4, 16) and (4, 16)
For f(-3) = f(3) = 9, the points are (-3, 9) and (3, 9)
For f(-1) = f(1) = 1, the points are (-1, 1) and (1, 1)
Notice that f(0) = 0^{2} = 0, so there is a single point (0,0)
Now, try to graph these seven points on a coordinate system.
(-4, 16), (4, 16), (-3, 9), (3, 9), (-1, 1), (1, 1), and (0, 0)
From the graph above, we can make the following two important observations:
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