Determining Symmetry (3.17.1)

Question 1

• Symmetry indicates that half the graph of a curve is an exact mirror image of the other half of the graph. You can take the right half of the curve and flip it over the y-axis to see the left half of the curve.

Answer 1

• Symmetry indicates that half the graph of a curve is an exact mirror image of the other half of the graph. You can take the right half of the curve and flip it over the y-axis to see the left half of the curve.

Question 2

• An even function is one which exactly maps one half of itself on the right side of its axis and exactly reflects that half on the left side of its axis; i.e., an even function is one which is symmetrical about its axis.

Answer 2

• An even function is one which exactly maps one half of itself on the right side of its axis and exactly reflects that half on the left side of its axis; i.e., an even function is one which is symmetrical about its axis.

Question 3

• An even function will pair each y-value used with both x and –x for every value used for x. This means that f (x) = f (–x) for these equations.

Answer 3

• An even function will pair each y-value used with both x and –x for every value used for x. This means that f (x) = f (–x) for these equations.

Question 4

• An odd function will be symmetrical but in respect to the origin, (0, 0). For an odd function, every point (x, y) will be matched with (–x, –y). You can take the right half of the curve and flip it over the y-axis, then flip it again over the x-axis to see the left half of the curve.

Answer 4

• An odd function will be symmetrical but in respect to the origin, (0, 0). For an odd function, every point (x, y) will be matched with (–x, –y). You can take the right half of the curve and flip it over the y-axis, then flip it again over the x-axis to see the left half of the curve.

Question 5

• For an odd function, every f (–x) = –f (x). Every –x-value is matched with its –y-value.

Answer 5

• For an odd function, every f (–x) = –f (x). Every –x-value is matched with its –y-value.

Question 6

• A circle is symmetrical with respect to the x-axis, the y-axis and also with the origin. Remember that a circle is not a function because it cannot pass the vertical line test.

Answer 6

• A circle is symmetrical with respect to the x-axis, the y-axis and also with the origin. Remember that a circle is not a function because it cannot pass the vertical line test.