By Marina Cohen
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In general. ) However, it is always true that |a + b| ≤ |a| + |b|. 7 The distance between a and b This is referred to as the triangle inequality. The interpretation of |a − b| as the distance between a and b (see the note in the margin) is particularly useful for solving inequalities involving absolute values. Wherever possible, we suggest that you use this interpretation to read what the inequality means, rather than merely following a procedure to produce a solution. 5 Solving an Inequality Containing an Absolute Value Solve the inequality 5 2 Ϫ 5 ϭ Ϫ3 |x − 2| < 5.
2. 30 provide a catalog of the possible types of graphs of cubic polynomials. , y = ax 4 + bx 3 + cx 2 + d x + e). Start by using your calculator or computer to sketch graphs with different values of a, b, c, d and e. Try y = x 4 , y = 2x 4 , y = −2x 4 , y = x 4 + x 3 , y = x 4 + 2x 3 , y = x 4 − 2x 3 , y = x 4 + x 2 , y = x 4 − x 2 , y = x 4 − 2x 2 , y = x 4 + x, y = x 4 − x and so on. Try to determine what effect each constant has. cls 26 .. 38 g = f −1 y 8 y ϭ x3 6 4 The number of common inverse problems is immense.
X − 1 = x 2 − 1 30. x 2 + 4 = x 2 + 2 31. x 3 − 3x 2 = 1 − 3x 32. x 3 + 1 = −3x 2 − 3x 1. Graph y = x 2 − 1, y = x 2 + x − 1, y = x 2 + 2x − 1, y = x 2 − x − 1, y = x 2 − 2x − 1 and other functions of the form y = x 2 + cx − 1. Describe the effect(s) a change in c has on the graph. 2. 30 provide a catalog of the possible types of graphs of cubic polynomials. , y = ax 4 + bx 3 + cx 2 + d x + e). Start by using your calculator or computer to sketch graphs with different values of a, b, c, d and e.