Chapter 4 Section 1

Notes

Linguistic Mapping Exercises

Knowledge Checks

  1. Determine which of the following functions are even, odd or neither:
    1. \(f(x)=x^2+\cos(x)\)
    2. \(f(x)=x^2+|x|+x\)
    3. \(f(x)=x^4\sin(x)\)
  2. Take \(f\) to be a function that is even. Part of its graph is shown below. Sketch what \(f\) looks like for values of \(x\) that are negative.

  1. Take \(f\) to be the function that is given by \[f(x)=|x-3|.\] Determine a vertical line \(L\) so that reflection of \(f\) across \(L\) is equal to \(f.\)
  2. Take \(f\) to be a function that is given by \[f(x)=|x-3|.\] Determine a vector \(\langle a,0\rangle\) so that \(\langle a,0\rangle+f\) is an even function.
  3. Take \(f\) to be a function that is given by \[f(x)=(x+2)|x+2|-1.\] Determine a point \(p\) so that rotation around \(p\) by half a circle equals \(f\).
  4. Take \(f\) to be a function that is given by \[f(x)=(x+2)|x+2|-1.\] Determine a vector \(V\) so that \(V+f\) is an odd function.

Practice Problems

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