Reflections of graphs along various lines.

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Presentation transcript:

Reflections of graphs along various lines. Precalculus Section 4.3 Reflect graphs and use symmetry to sketch graphs Reflections of graphs along various lines. The graph of y = -f(x) is the graph of y = f(x) reflected in the x-axis.

The graph of y = |f(x)| is identical to the graph of y = f(x) when f(x) > 0 and identical to the graph of y = -f(x) when f(x)<0.

The graph of y = f(-x) is the graph of y = f(x) reflected in the y-axis.

The graph of x = f(y) is the graph of y = f(x) reflected in the line y=x.

Graph the following functions.

Tests for symmetry in various axes Symmetry in the y-axis: (-x,y) is on the graph whenever (x,y) is Symmetry in the x-axis: (x,-y) is on the graph whenever (x,y) is.

Test for symmetry in the origin: (-x,-y) is on the graph whenever (x,y) is. Test for symmetry in the line y = x: (y,x) is on the graph whenever (x,y) is.

Test for symmetry in the: x-axis y-axis line y=x origin x3 + y3 = 1

assign Page 136 Problems 1-8, 16