3.17.1 Determining Symmetry

Question 1

Symmetry

Answer 1

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

even function

Answer 2

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

odd function

Answer 3

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.