Worksheet: Even and Odd Functions

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In this worksheet, we will practice deciding whether a function is even, odd, or neither both from a graph of the function and from its rule.

Q1:

Is the function represented by the figure even, odd or neither even nor odd?

  • Aneither even nor odd
  • Bodd
  • Ceven

Q2:

Is the function 𝑓 ( 𝑥 ) = 4 𝑥 − 3 even, odd, or neither even nor odd?

  • Aeven
  • Bodd
  • Cneither even nor odd

Q3:

If a function is even, then its curve is symmetric about what?

  • Athe 𝑦 -axis
  • Bthe 𝑥 -axis
  • Cthe origin point

Q4:

If a function is odd, then its curve is symmetric about what?

  • Athe 𝑥 -axis
  • Bthe 𝑦 -axis
  • Cthe origin point

Q5:

Is the function represented by the figure even, odd, or neither even nor odd?

  • Aneither even nor odd
  • Bodd
  • Ceven

Q6:

Determine whether the function 𝑓 ( 𝑥 ) = 9 𝑥 is even, odd, or neither even nor odd, given that 𝑓 ∶ ( − 7 , 7 ] → ℝ .

  • Aeven
  • Bodd
  • Cneither even nor odd

Q7:

Determine whether the function 𝑓 is even, odd, or neither, given that 𝑔 ( 𝑥 ) = − 9 𝑥 − 8 𝑥 < 0 , 9 𝑥 − 8 𝑥 ≥ 0 . i f i f

  • Aneither even nor odd
  • Bodd
  • Ceven

Q8:

Determine whether the function 𝑓 ( 𝑥 ) = 8 𝑥 𝑥 < 0 , − 8 𝑥 𝑥 ≥ 0 , is even, odd, or neither.

  • Aodd
  • Bneither even nor odd
  • Ceven

Q9:

Determine whether the function represented by the following figure is even, odd, or neither even nor odd.

  • Aodd
  • Bneither even nor odd
  • Ceven

Q10:

Is the function represented by the figure even, odd or neither even nor odd?

  • Aneither even nor odd
  • Beven
  • Codd

Q11:

Which of the following points form an odd function?

  • A ( − 8 , − 8 ) , ( − 3 , − 6 ) , ( 0 , 3 ) , ( 3 , 6 ) , ( 8 , 8 )
  • B ( − 8 , − 8 ) , ( − 3 , − 6 ) , ( 0 , 3 ) , ( 3 , − 6 ) , ( 8 , − 8 )
  • C ( − 8 , − 8 ) , ( − 3 , − 6 ) , ( 0 , 0 ) , ( 3 , − 6 ) , ( 8 , − 8 )
  • D ( − 8 , − 8 ) , ( − 3 , − 6 ) , ( 0 , 0 ) , ( 3 , 6 ) , ( 8 , 8 )

Q12:

How can you tell from a graph that a function is odd?

  • A The graph is mirror-symmetric in the 𝑦 -axis.
  • B The values of the function are all odd numbers.
  • C There is no way you can tell.
  • D None of the points on the graph have an even 𝑦 -coordinate.
  • E The graph has point symmetry about the origin.

Q13:

How can you tell from a graph that a function is even?

  • AThe graph is mirror-symmetric in the 𝑦 -axis.
  • BNone of the points on the graph have an odd 𝑦 -coordinate.
  • CThe graph has point symmetry in the origin.
  • DThere is no way you can tell.
  • EThe values of the function are all even numbers.

Q14:

Is the function 𝑓 ( 𝑥 ) = 2 𝑥 − 1 5 𝑥 even, odd, or neither even nor odd?

  • ANeither even nor odd
  • BOdd
  • CEven

Q15:

Determine whether the function 𝑓 ( 𝑥 ) = − 9 𝑥 , where 𝑓 ∶ ℝ ⟶ ℝ , is even, odd, or neither even nor odd.

  • Aeven
  • Bodd
  • Cneither even nor odd

Q16:

Suppose that 𝐾 ( 𝑥 ) = 𝑥 is an even function, where 𝑛 ≥ 0 is an integer. What can be said about 𝑛 ?

  • A 𝑛 is an even number.
  • BNothing can be deduced about 𝑛 .
  • CThere is no such 𝑛 .
  • D 𝑛 can be any number.
  • E 𝑛 is an odd number.

Q17:

Is the function 𝑓 ( 𝑥 ) = 𝑥 6 𝑥 t a n even, odd, or neither even nor odd?

  • ANeither even nor odd
  • BOdd
  • CEven

Q18:

Is the function 𝑓 ( 𝑥 ) = 8 𝑥 + 8 𝑥 ∀ 𝑥 ∈ ℝ even, odd, or neither even nor odd?

  • Aeven
  • Bneither even nor odd
  • Codd

Q19:

Determine whether the function 𝑓 ( 𝑥 ) = 𝑥 , where 𝑥 ∈ ℝ − { − 6 } , is even, odd, or neither even nor odd.

  • Aneither even nor odd
  • Beven
  • Codd

Q20:

Is the function 𝑓 ( 𝑥 ) = 4 𝑥 + 5 + 2 even, odd or neither even nor odd?

  • Aodd
  • Bneither even nor odd
  • Ceven

Q21:

Which of the following points form a curve that represents an even function?

  • A ( − 6 , 8 ) , ( − 5 , 7 ) , ( 0 , 1 ) , ( 5 , − 7 ) , ( 6 , − 8 )
  • B ( − 6 , − 8 ) , ( − 5 , − 7 ) , ( 0 , 1 ) , ( 5 , − 8 ) , ( 6 , − 7 )
  • C ( − 6 , − 8 ) , ( − 5 , − 7 ) , ( 0 , 0 ) , ( 5 , 7 ) , ( 6 , 8 )
  • D ( − 6 , − 8 ) , ( − 5 , − 7 ) , ( 0 , 1 ) , ( 5 , − 7 ) , ( 6 , − 8 )

Q22:

Is the function 𝑓 ( 𝑥 ) = √ 2 𝑥 − 3 even, odd or neither even nor odd?

  • Aneither even nor odd
  • Bodd
  • Ceven

Q23:

Is the function 𝑓 ( 𝑥 ) = − 𝑥 − 3 𝑥 − 8 𝑥 ∀ 𝑥 ∈ ℝ even, odd, or neither even nor odd?

  • Aodd
  • Bneither even nor odd
  • Ceven

Q24:

Is the function 𝑓 ( 𝑥 ) = 6 𝑥 6 𝑥 + 9 even, odd or neither even nor odd?

  • Aodd
  • Bneither even nor odd
  • Ceven

Q25:

Is the function 𝑓 ( 𝑥 ) = 7 𝑥 + 2 − 7 ≤ 𝑥 < 0 , 2 − 7 𝑥 0 ≤ 𝑥 ≤ 7 , i f i f even, odd, or neither even nor odd?

  • Aodd
  • Beven
  • Cneither even nor odd

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