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Even and odd functions worksheets Grade 10

Find f(−x) and decide whether a function is even, odd or neither.

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How to do it

Find f(−x). If it equals f(x), f is even. If it equals −f(x), f is odd. Otherwise it is neither.

f(x)=−x3−6x2−3x+4even, odd, or neither: neitherf(x) = -x^{3} - 6x^{2} - 3x + 4\quad \text{even, odd, or neither: }\text{neither}
f(−x)=−(−x)3−6(−x)2−3(−x)+4=x3−6x2+3x+4f(-x) = -(-x)^{3} - 6(-x)^{2} - 3(-x) + 4 = x^{3} - 6x^{2} + 3x + 4put −x in for x
f(−x) is neither f(x) nor −f(x)f(-x)\ \text{is neither }f(x)\ \text{nor }-f(x)

Example problems

  1. f(x)=−4x3−5xeven, odd, or neither: f(x) = -4x^{3} - 5x\quad \text{even, odd, or neither: }
  2. f(x)=x4+4x2−3even, odd, or neither: f(x) = x^{4} + 4x^{2} - 3\quad \text{even, odd, or neither: }
  3. f(x)=2x3+3x2−6x+5even, odd, or neither: f(x) = 2x^{3} + 3x^{2} - 6x + 5\quad \text{even, odd, or neither: }
  4. f(x)=−5x3−4x2−2x+6even, odd, or neither: f(x) = -5x^{3} - 4x^{2} - 2x + 6\quad \text{even, odd, or neither: }

Functions

  1. Evaluating functions
  2. Finding the domain of a function
  3. Adding, subtracting and multiplying functions
  4. Composition of functions
  5. Inverse functions
  6. Transformations of functions
  7. Even and odd functions
  8. Average rate of change