26. The graph of the function g with g(x) = 23:43) from Example 2 in this lesson seems to be a hyperbola. Use algebra to show that the graph is a translation image of the hyperbola with equation xy = l 2. Example 2 Rewrite the expression x2 - x - 12 in lowest terms. 2x2 - 18 Solution 1 x2 - x- 12 (x + 3)(x - 4) 2x2 - 18 = 2(x + 3)(x - 3) Factor each polynomial to see if there are common factors. x +3 x - 4 = x+ 3 2(x - 3) Multiplication of Fractions Property =1. X-4 2(x - 3) A number divided by itself is 1. X - 4 = 2(x - 3) Multiplication Property of 1 Solution 2 Using a CAS produced the same expression, but it also produced a warning about the domain. Is x2-x-12 x-4 2x2 - 18 the domain of * -* - 12 the same as the domain 2.x2-18 2.(.1-3) X - 4 Of 2(X - 3) . Check Use the Means-Extremes Property. A Domain of the result might be larger th... Does 2(x - 3)(x2 - x - 12) = (2x2 - 18)(x - 4)? Either multiplication of the polynomials or factoring shows the expressions to be equivalent. The original and final expressions in Example 2 are equivalent: x2 - x - 12 _ x -4 .We say that this equation is an identity. 2x2 - 18 2(x - 3)