worked example even, odd, neither even nor odd function
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Worked example Even, Odd, Neither even nor odd functionTRANSCRIPT
Test to determine if a function is even, odd or neither
1
Mathematics Section Universiti Kuala Lumpur Malaysia France Institute
How to determine if a function is even, odd or neither when the FUNCTION is given
algebraically, )x(fy
To test whether a function )x(fy is even, odd or neither even nor odd, replace x with x
and compare the result to )x(f
If )x(f)x(f then the function )x(f is even
If )x(f)x(f then the function )x(f is odd
If )x(f)x(f and )x(f)x(f then the function )x(f is neither even nor odd
Example 1
Determine whether 7x3x)x(f 24 is even, odd or neither even nor odd function.
STEP 1: Replace x with -x
7x3x)x(f 24
7)x(3)x()x(f 24
STEP 2: Recalculate
7x3x)x(f 24
STEP 3: Compare the result to )x(f
)x(f 7x3x 24 )x(f
STEP 4: Conclusion
Since )x(f)x(f , the function 7x3x)x(f 24 is
an EVEN function
Test to determine if a function is even, odd or neither
2
Mathematics Section Universiti Kuala Lumpur Malaysia France Institute
Example 2
Determine whether xx
4x)x(f
3
2
is even, odd or neither even nor odd function.
STEP 1: Replace x with -x
xx
4x)x(f
3
2
)x()x(
4)x()x(f
3
2
STEP 2: Recalculate
xx
4x)x(f
3
2
STEP 3: Compare the result to )x(f
xx
4x)x(f
3
2
)x(f
Conclusion:
Since )x(f)x(f , the function xx
4x)x(f
3
2
is NOT
AN EVEN function
STEP 4: Try to factor out 1
xx
4x
)xx(
4x)x(f
3
2
3
2
STEP 5: Compare the result to )x(f
xx
4x)x(f
3
2
)x(f
STEP 6: Conclusion Since )x(f)x(f , the function
xx
4x)x(f
3
2
is an
ODD function
Test to determine if a function is even, odd or neither
3
Mathematics Section Universiti Kuala Lumpur Malaysia France Institute
Example 3
Determine whether 8x3x)x(f 35 is even, odd or neither even nor odd function.
STEP 1: Replace x with -x
8x3x)x(f 35
8)x(3)x()x(f 35
STEP 2: Recalculate
8x3x)x(f 35
STEP 3: Compare the result to )x(f
8x3x)x(f 35 )x(f
Conclusion:
Since )x(f)x(f , the function 8x3x)x(f 35 is
NOT AN EVEN function
STEP 4: Try to factor out 1
)8x3x(8x3x)x(f 3535
STEP 5: Compare the result to )x(f
)8x3x()x(f 35 )x(f
Conclusion:
Since )x(f)x(f , the function 8x3x)x(f 35 is
NOT AN ODD function
STEP 6: Conclusion
Since )x(f)x(f and )x(f)x(f , the function
8x3x)x(f 35 is NEITHER even nor odd
function
Test to determine if a function is even, odd or neither
4
Mathematics Section Universiti Kuala Lumpur Malaysia France Institute
How to determine if a function is even, odd or neither when the GRAPH of the
function is given
Any function with a graph symmetric about the y-axis is an EVEN function
Any function with a graph symmetric about the origin is an ODD function
Any function with a graph NON symmetric about the y-axis or the origin is a
NEITHER EVEN NOR ODD function
Example 4
Based on the following graphs, determine whether the function is even, odd or neither even nor
odd function.
(a)
(b)
(c)
Since the graph is symmetric about the y-axis, the function is even.
Since the graph is symmetric about the origin, the function is odd.
Since the graph is NOT symmetric about the y-axis and the origin, the function is neither even nor odd.