Symmetry Answers
✔ line symmetry onlyrotational symmetry onlyno symmetryboth line and rotational symmetry
line symmetry only✔ rotational symmetry onlyno symmetryboth line and rotational symmetry
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This graph shows a portion of an even function. Use the graph to complete the table of values.
✔ evenoddneither
(f • g)(x) =evenoddneither
The function is increasingdecreasing✔ constant for –9 < x < –7.
✔ line symmetry onlyrotational symmetry onlyno symmetryboth line and rotational symmetry
This graph shows a portion of an odd function.
Dimetri says that a function that is made of terms where the variable is raised only to an odd power will be an odd function. Do you agree with Dimetri? Explain why or why not.
Dimetri is correct only if there is no constant term. For every odd-power term, replacing x with −x makes the term its opposite because (−x) raised to an odd power equals −x raised to that power. A constant term does not change, so it prevents the function from being odd.
Compare your response to the sample response above. Did your explanation
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g(x) = |x-3| evenodd✔ neither
(g • g)(x) = evenoddneither
The function is increasing for –3 < x < 0✔ –7 < x < –3–9 < x < –7.
line symmetry only✔ rotational symmetry onlyno symmetryboth line and rotational symmetry
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