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10 cards from this deck
y=−f(x)y = -f(x)y=−f(x) flips the graph across the xxx-axis.
It maps (x,y)(x, y)(x,y) to (x,−y)(x, -y)(x,−y) on the transformed graph.
All positive yyy-values become negative and vice versa.
y=f(−x)y = f(-x)y=f(−x) reflects the graph across the yyy-axis.
It maps (x,y)(x, y)(x,y) to (−x,y)(-x, y)(−x,y) on the transformed graph.
y=−f(−x)y = -f(-x)y=−f(−x) rotates the graph 180 degrees around the origin.
The reflection is not defined since x\sqrt{x}x is for x≥0x \geq 0x≥0.
y=−x2+4x−3y = -x^2 + 4x - 3y=−x2+4x−3 after reflecting across the xxx-axis.
It returns to the original function 1/x1/x1/x after reflections.
They help predict and analyze functions’ behavior.
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