Graphing Rational Functions Through Transformations.

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Presentation transcript:

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 H(x)=f(x+c)horizontal shift c units to the left H(x)=f(x)-cvertical shift c units downward H(x)=f(x)+cvertical shift c units upward

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

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.

Graphing based on transformations Tell the transformations that occurred and graph the following

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

Graphing based on transformations Tell the transformations that occurred and graph the following

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