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Graphing Rational Functions Through Transformations

Graphing Rational Functions Through Transformations. Rational parent function. Vertical and horizontal shifts. The following changes in the functions y=f(x) will produce the stated shifts in the graph of y=f(x): H(x)=f( x-c ) horizontal shift c units to the right

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Graphing Rational Functions Through Transformations

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  1. Graphing Rational Functions Through Transformations

  2. Rational parent function

  3. Vertical and horizontal shifts • The following changes in the functions y=f(x) will produce the stated shifts in the graph of y=f(x): • H(x)=f(x-c) horizontal shift c units to the right • H(x)=f(x+c) horizontal shift c units to the left • H(x)=f(x)-c vertical shift c units downward • H(x)=f(x)+c vertical shift c units upward

  4. Reflections • The following changes in the function y=f(x) will produce the stated reflections in the graph of y=f(x): • H(x)=-f(x) reflection with respect to the x-axis • H(x)=f(-x) reflection with respect to the y-axis

  5. Nonrigid transformations • Nonrigid transformations actually distort the shape of the graph, instead of just shifting or reflecting it. • Nonrigid transformations of y=f(x) come from equations of the form y=cf(x). • If c>1, then there is a vertical stretch of the graph of y=f(x). • If 0<c<1, then there is a vertical shrink • We will discuss horizontal extensions and compressions at a further date.

  6. Graphing based on transformations • Tell the transformations that occurred and graph the following

  7. Answer • Transformations and graph • Up 3 (HA), right 5 (VA), reflect over x-axis, and stretch by 2

  8. Graphing based on transformations • Tell the transformations that occurred and graph the following

  9. Answer • Transformations and graph • Down 4 (HA), left 2 (VA), reflect over x-axis

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