2.1 Who is the Fairest of Them All?

Who is the Fairest of Them All?
Symmetry in  everyday language refers to a sense of harmonious and beautiful proportion and balance. There’s even research says that we rate symmetric faces as being more attractive! Let's investigate further what it means for functions to be symmetric and how we might predict the symmetry of a graph from its equation.

The graph of f(x)=x^{2}-2 is below. 

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What do you notice about the symmetry of f?

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Fill in the table of values for f.

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What patterns do you notice in the ordered pairs?

The graph of g(x)=x^{3}-4x is below. 

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What do you notice about the symmetry of g?

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Fill in the table of values.

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What patterns do you notice in the ordered pairs?

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Do you remember the names of the types of symmetry you learned in Algebra?

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What do you notice about the symmetry of f?

Fill in the table of values for f.

What patterns do you notice in the ordered pairs?

What do you notice about the symmetry of g?

Fill in the table of values.

What patterns do you notice in the ordered pairs?

Do you remember the names of the types of symmetry you learned in Algebra?

How can you check for these types of symmetry without a graph?