Lesson Worksheet: Even and Odd Functions Mathematics

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?

  • Aeven
  • Bneither even nor odd
  • Codd

Q2:

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

  • Aeven
  • Bneither even nor odd
  • Codd

Q3:

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

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

Q4:

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

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

Q5:

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

  • Aeven
  • Bodd
  • Cneither even nor odd

Q6:

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

  • Aeven
  • Bneither even nor odd
  • Codd

Q7:

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

  • Aeven
  • Bneither even nor odd
  • Codd

Q8:

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

  • Aeven
  • Bneither even nor odd
  • Codd

Q9:

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

  • Aeven
  • Bneither even nor odd
  • Codd

Q10:

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

  • Aeven
  • Bneither even nor odd
  • Codd

Q11:

Which of the following points form an odd function?

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

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

Q13:

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

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

Q14:

Is the function 𝑓(𝑥)=2𝑥−15𝑥 even, odd, or neither even nor odd?

  • AOdd
  • BEven
  • CNeither even nor odd

Q15:

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

  • Aeven
  • Bneither even nor odd
  • Codd

Q16:

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

  • A𝑛 is an odd number.
  • B𝑛 is an even number.
  • CNothing can be deduced about 𝑛.
  • D𝑛 can be any number.
  • EThere is no such 𝑛.

Q17:

Is the function 𝑓(𝑥)=𝑥6𝑥tan even, odd, or neither even nor odd?

  • AEven
  • BOdd
  • CNeither even nor odd

Q18:

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

  • Aeven
  • Bodd
  • Cneither even nor odd

Q19:

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

  • Aneither even nor odd
  • Bodd
  • Ceven

Q20:

Is the function 𝑓(𝑥)=4𝑥+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), (0,0), (5,7), (6,8)
  • B(−6,−8), (−5,−7), (0,1), (5,−8), (6,−7)
  • C(−6,8), (−5,7), (0,1), (5,−7), (6,−8)
  • D(−6,−8), (−5,−7), (0,1), (5,−7), (6,−8)

Q22:

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

  • Aneither even nor odd
  • Beven
  • Codd

Q23:

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

  • Aneither even nor odd
  • Bodd
  • Ceven

Q24:

Is the function 𝑓(𝑥)=6𝑥6𝑥+9 even, odd or neither even nor odd?

  • Aeven
  • Bodd
  • Cneither even nor odd

Q25:

Is the function 𝑓(𝑥)=7𝑥+2−7≤𝑥<0,2−7𝑥0≤𝑥≤7,ifif even, odd, or neither even nor odd?

  • Aodd
  • Beven
  • Cneither even nor odd

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