College Algebra, 2013a

96 Relations and Functions
1.
f(x) =
f(−x) =
f(−x) =
f(−x) = f(x)
5
2 − x 2
5
2 − (−x) 2
5
2 − x 2
Hence, f is even. The graphing calculator furnishes the following.
This suggests 4 that the graph of f is symmetric about the y-axis, as expected.
2.
g(x) =
5x
2 − x 2
g(−x) =
5(−x)
2 − (−x) 2
g(−x) = −5x
2 − x 2
It doesn’t appear that g(−x) is equivalent to g(x). To prove this, we check with an x value.
After some trial and error, we see that g(1) = 5 whereas g(−1) = −5. This proves that g is
not even, but it doesn’t rule out the possibility that g is odd. (Why not?) To check if g is
odd, we compare g(−x) with−g(x)
Hence, g is odd. Graphically,
4 ‘Suggests’ is about the extent of what it can do.
−g(x) = − 5x
2 − x 2
= −5x
2 − x 2
−g(x) = g(−x)